







A pond in a garden 
20200409 

From Jin: c) I have a large square pond set inside a square garden: both the pond and the
garden have sides which are a whole number of metres, and outside the pond,
the garden is grassed over. The area covered by grass is 188 square metres.
Find the area of the pond. (5 marks) Answered by Penny Nom. 





An arithmetic sequence 
20200404 

From ally: 10 ... last term 35 common difference is 3
(a) find the number of term in the sequence.
i have lost the formula. Answered by Penny Nom. 





The difference between two number is 7 
20200107 

From Jaypercey: the difference between two number is 7 find the two number if the larger 3times the smaller Answered by Penny Nom. 





An arithmetic sequence 
20190223 

From Dalal: If x+1 and x+17 are the second and sixth term of a sequence with a common difference of 5, what's the value of x. Answered by Penny Nom. 





An arithmetic sequence 
20190131 

From sara: if the 6th term of an arithmetic sequence is 8 and the 11th term is 2, what is the first term? Answered by Penny Nom. 





The sum and difference of two numbers 
20180830 

From Saranya: Hi,
The question is to find the numbers from sum and difference.
The Sum = 14 and the difference = 2
I found in this web site some useful answers. but my kid is going second grade only. She don't know how to do a division or multiplication.
So can you please explain on how to find the answer using only the Addition and Subtraction.
Thanks in advance. Answered by Penny Nom. 





The difference between two numbers is 3 
20180605 

From Hannah: write a pair if integers whose difference is 3 ( given that the greater number is 8 ) Answered by Penny Nom. 





Pre tax and post tax percentages 
20180522 

From Tom: Hi,
I work in a clothes shop which can also do mailorders. My Head Office
has sent a report with which we can check the records we keep in store
tally with those at HO.
According to that report we have taken £2578.25 in orders, excluding VAT (20%),
which would therefore be £3093.91 including VAT (2578.25+20%=3093.91).
According to my records, we have taken £3179.32 including VAT, which would be
£2543.45 excluding VAT (3179.3220%=2543.45).
Why is it that the difference between the VAT inclusive figures (3179.323093.91) is +£85.41, but
the difference between the VAT exclusive figures (2543.452578.26) is £34.81?
Now, I can see from the report that 1 order has not been recorded by HO, and I
know that our average order value is around £30, so the £34.81 makes sense.
But surely both figures should be a minus, regardless of whether they include VAT?
I'm sure there is an obvious answer, but I just cannot see it! Any help would be gratefully
received.
Thanks,
Tom Answered by Penny Nom. 





The sum and difference of two numbers 
20180313 

From samima: Two numbers have a difference of 0.85 and the sum 1.What are the numbers? Answered by Penny Nom. 





Expand (5x9)(5x+9) 
20180301 

From adil: expand the following:
(5x9)(5x+9) Answered by Penny Nom. 





The sum and difference of two numbers 
20180125 

From Ali:
Hello,
I was looking at the original question that was posted and answered by
your team:
http://mathcentral.uregina.ca/QQ/database/QQ.09.07/s/donna1.html
I used the 7 and 4 as example and not looking for 39 per original
question:
A=7
B=4
7+ 4 =11 and 74 = 3
We end up with 11 +3 = 14
A= 14/2 give use 7
B = how do you solve for B or 4 with out knowing anything about 3 or any other numbers ?
Thank you
Ali Answered by Penny Nom. 





An arithmetic sequence 
20171130 

From yo: x; 2x+1; 11 are three consecutive terms of an arithmetic sequence.calculate x Answered by Penny Nom. 





An arithmetic sequence 
20170717 

From abbi: hi there im a student in 11 grade
ive been trying to do this task but i have no idea how to do it
the question is
Find the common difference and the n^th term of the arithmetic sequence if the first term is 4 and the twentieth sum of the terms is 1030 Answered by Penny Nom. 





Successive Differences 
20170406 

From Twaha: Please find the equation of the sequence 1 2 4 7 11 16 22 Answered by Penny Nom. 





The sum and difference of two numbers 
20170320 

From Olivia: The sum of two numbers is 87 and their difference is 29. What are the two numbers Answered by Penny Nom. 





1/1cosine(2x)  1/1+ cos(2x) 
20161214 

From Sean: 1/1cosine(2x)  1/1+ cos(2x) Answered by Penny Nom. 





A pattern rule for a sequence 
20161028 

From Grace: Here's a Grade 7 question, we need to find the pattern rule:
1  1
2  3
3  6
4  10
......
It may involve exponents, but we can't seem to figure it out.
thank you.
Grace. Answered by Penny Nom. 





A sequence 
20160105 

From Mia: the next three terms in each sequence. 0.4, 0.54, 0.68, 0.82, Answered by Penny Nom. 





2^48  1 
20150613 

From Soham: The number 2^481 is divisible by two numbers between 60 and 70. The sum of
the two numbers is? Answered by Penny Nom. 





A limit 
20150219 

From genc: Lim (27x^31) / (3x1)
X> 1/3 Answered by Harley Weston. 





A difference quotient 
20150112 

From Sasha: Simplify the difference quotient
f(x) − f(a)/ xa
if x ≠ a.
f(x) = x^3 − 12
Answered by Penny Nom. 





(x3)^2(x+3)^2 
20141113 

From Bernice: (x3)^2(x+3)^2 Answered by Penny Nom. 





An arithmetic sequence 
20140320 

From Xabiso: The 10th term of an arithmetic sequence is 28 and the 7th term is 19. Calculate the common difference and the first term of the sequence. Answered by Penny Nom. 





Can 100r^281z^2 be factored? 
20131208 

From Rosa: Can 100r^281z^2 be factored? Answered by Penny Nom. 





An Arithmetic Progression 
20131008 

From collins: In an A.P. the difference between the 8th and 4th term is 20 and the 8th is one and half times the 4th term... what is the common difference and the first term Answered by Penny Nom. 





Constructing a triangle 
20130822 

From Nazrul: The base, the difference of the angles adjoining the base and the sum of the other
two sides are given. How can I draw the triangle?
Please help me. Answered by Chris Fisher. 





a cubeb cubea+b= ? 
20130616 

From saryu: a cubeb cubea+b= ?
find the answer Answered by Penny Nom. 





Two numbers whose difference is 16 
20130608 

From Johan: Two numbers whose difference is 16 and whose sum is 120 Answered by Penny Nom. 





(4 4cos^4 x)/(sin^2 x) 
20130518 

From Agnes: How I can solve this question :
Simplify (4 4cos^4 x)/(sin^2 x) and write in terms of sin x Answered by Penny Nom. 





An algebraic exercise 
20130318 

From autumn: given: f(x)=x/(x^2+2) determine: [f(xh)f(x)]/h Answered by Penny Nom. 





Difference of squares 
20121119 

From Qelibar: Please factorise x^2y^2  4 Answered by Penny Nom. 





The difference of the numbers on two dice 
20120819 

From dilys: Two fair dice are thrown. Find the probability that the difference of the two numbers is divisible by 4? Answered by Chris Fisher and Lorraine Dame. 





Two equations involving fractions 
20120612 

From Fatima: Hi ,teacher gave two question to my daughter as follows
Solve 2/x+3=(1/xx9)(1/x3)and
Solve (4/x2)(x/x+2)=16/xx4
Please help me
Thanks & regards fatima Answered by Penny Nom. 





The difference in latitudes of two cities 
20120118 

From Renee: Assuming that the earth is a sphere of radius 6378 kilometers, what is the difference in latitudes of two cities, one of which is 600 kilometers due north of the other? Answered by Robert Dawson. 





Sum and difference of squares 
20111231 

From Anne: Se x e y são números reais distintos, então:
a) (x^2 + y^2) / (x  y) = x + y
b) (x^2 + y^2) / (x  y) = x  y
c) (x^2  y^2) / (x  y) = x + y
d) (x^2  y^2) / (x  y) = x  y
e) Nenhuma das alternativas anteriores é verdadeira. Answered by Harley Weston. 





U(n+1) = 2Un + 1 
20110522 

From Cillian: In a certain sequence, to get from one term to the other you multiply by 2 and add 1, i.e. This is a difference equation of form: U(n+1) = 2Un + 1. prove that there is a maximum of 2 perfect squares in this sequence Answered by Claude Tardif. 





Find two numbers whose difference is 153. 
20110510 

From Scott: Find two numbers whose difference is 153. Answered by Penny Nom. 





(3x+4y)^2  (2xy)^2 
20110316 

From Taiwo: pls could some one help me with this question? thanks as lot
factorize:
(3x+4y)^2  (2xy)^2 Answered by Penny Nom. 





Difference quotient 
20100726 

From Brandon: i'm trying to figure out how to use the difference quotient with x^3, i have tried the following...(x+h)^2*(x+h)(x+h)/h and i have only gotten as far as...(x^2+2xh+h^2)(x+h)/h....i cannot see where i am goin astray, i know i am overlooking something simple, what am i overlooking? Answered by Penny Nom. 





Difference of cubes 
20100522 

From Anad: how can we prove a^3  b^3 is equal to (ab)(a^2+ab+b^2)? Answered by Penny Nom. 





(9  x^2)/(x  3) 
20091204 

From Sandy: 9x^2/x3
I need to know how to solve this.
Thanks Answered by Penny Nom. 





Successive differences 
20090618 

From Jonathan: I'm trying to find the next number sequence for this equation: 1 11 35 79 149 251, my problem is that I worked it out and ended up with a single number 17. What am I doing wrong. Thank you for any help. Answered by Robert Dawson and Penny Nom. 





A difference quotient 
20090617 

From Sue: When s(x)=x^3+x, compute and simplify the difference quotient s(x+h)s(x)/h. Answered by Harley Weston. 





Actual Food Cost is 3% or more above Projected Food Cost 
20090407 

From Kam: Your store guidelines states that when Actual Food Cost is 3% or more above Projected Food Cost, immediate corrective action be taken by the Unit Manager. In January, your Actual Food Cost was $11,000, and your Projected Food Cost was $10,850. To find out what percentage the difference is do I divide the difference ($150) by Actual Food Cost ($11,000) or Projected Food Cost ($10,8500)? What would be the answer? Thanks Answered by Harley Weston. 





Percentage difference in pipe volumes 
20090222 

From mike: what is the % difference between a 3 inch diameter pipe compared to a 4 inch diameter pipe? and how do i find the answer? Answered by Penny Nom. 





The difference quotient (f(x+h)f(x))/h 
20090126 

From helen: Find the difference quotient of f, f(x+h)f(x)/h, h does not equal 0, for this function. Be sure to simplify. that is, find f(x)=x^2x+4 Answered by Robert Dawson. 





Factor x^2  y^2 
20090120 

From Shell: complete Factor: x^2y^2 Answered by Penny Nom. 





Determining the Unknown Numbers 
20081206 

From jacob: the sum of two numbers is 45 and their difference is 15. what are the two numbers? Answered by Janice Cotcher. 





Factoring 
20081119 

From Neji: How do you factor (yz) (y+z) (y^4+y^2z^2+z^4) and get (y+z)(y^2yz+z^2) (yz) (y^2+yz+z^2) as the answer? Answered by Harley Weston. 





z(z+1)x(x+1) / zx 
20080930 

From sylvia: z(z+1)x(x+1) / zx
HOW DO I SIMPLIFY THIS Answered by Penny Nom. 





a(a+1)  b(b+1) 
20080930 

From Shaun: I need to factor (ab) out of the following: a(a+1)  b(b+1). I know it is simple but I cannot remember how. Answered by Penny Nom. 





3,6,10,15,and 21 
20080928 

From jarred: i am currently stumped on a math project that requires me to find out the recursive formula for a sequence of numbers. the numbers in the sequence are 3,6,10,15,and 21. Thank you for your time. Answered by Walter Whiteley. 





A cubic equation 
20080825 

From RAM: The following Cubic Eqn should have three roots  what are they?
x^327=0 Answered by Penny Nom. 





Simplifying Algebraic Expressions 
20080822 

From Jacky: x^2y^2+4x+4y Answered by Penny Nom. 





Factoring x^2 + 729 
20080819 

From peter: hello I,am having trouble factorising a polynomial into polynomial factors
with real coefficients please can you help the polynomial is x^2+729 Answered by Harley Weston. 





[f(x)f(1)]/(x1) 
20080814 

From katie: Evaluate (if possible) the function of the given value of the independent
variable:
f(x)=(x^3)x:
[f(x)f(1)]/(x1) Answered by Penny Nom. 





Percent difference 
20080812 

From mike: What is the percent difference between two homes if one is worth $525,000
and the other is $425,000. (525,000  425,000 = 100,000) Answered by Penny Nom. 





A difference quotient 
20080710 

From Rita: Find the difference quotient of f, that is, find [f (x + h)  f (x)]/h, where
h does not = 0 for the given function. Be sure to simplify.
f(x) = 1/(x + 3) Answered by Janice Cotcher. 





Percent difference? 
20080614 

From Cathy: I am trying to verify a "percent of difference" as stated on a tax form. I cannot seem to come up with the equation to do so.
Here are a few examples on the form:
Last year $62.91 this year $66.05 tax difference $3.14 percent difference 5.64%
Last year $ 2014.97 this year $1982.93 tax difference $32.04 percent difference 57.56%
Last year $97.66 this year $79.58 tax difference $18.08 percent difference 32.48%
I have tried several different ways and per some of Q&A's already on your site I still have a problem and would appreciate some assistance.
ThanksCathy Answered by Penny Nom. 





Percentage difference 
20080520 

From Cavell: Hi, the projected cost was 71,700. The actual cost was 56,876. What is the percent difference? Answered by Penny Nom. 





5x^2  45 
20080211 

From Tiana: factor:
5x^2  45 Answered by Stephen La Rocque. 





Sum and difference of cubes 
20080130 

From Amanda: It has been a really long time since I was in Algebra and I can't remember how to factor cubes such as x^3 +81 or subtracting/adding fractions with variables such as [1/(x+h)+2][1/x+2]. Please help!!! Answered by Penny Nom. 





Percentage of what? 
20080123 

From Jenny: What is the difference in percentage between 31990 and 29990? Answered by Stephen La Rocque. 





Explaining the factoring for the difference of cubes 
20080116 

From Bill: A student asked me where did the "difference of cubes" and "sum of cubes" come from. I did not have an answer for her. She is very bright and understands how they work but wanted to know where they derived from. Any help you can offer would be great. Thanks Answered by Stephen La Rocque. 





Expand (a^4  b^4) 
20071117 

From Saif: how would you expand (a^4  b^4) ??? Answered by Stephen La Rocque and Victoria West. 





The nth term 
20071018 

From shannon: Ok , what i am having problems with is the nth term. I get how the numbers come together, but i am having trouble with finding the nth term. Answered by Penny Nom. 





The percentage difference between 1/20 to 1/15 
20071011 

From jake: what is the percentage difference between 1/20 to 1/15.... Answered by Stephen La Rocque. 





Sum and difference of two mystery numbers 
20071004 

From Donna: The sum of two numbers is 39. The difference is 11. What are the numbers? Answered by Stephen La Rocque. 





Percentage differences 
20070829 

From Camilla: If a store sells a certain syle of skirt, an in the first week they sell 13,
in the second week 20, in the third week 17 and in the fourth week 23, calculate the percentage
difference between the highest and the lowest weekly sale. Answered by Stephen La Rocque and Harley Weston. 





Percentage difference between a microcentury and 50 minutes 
20070821 

From Wonder: A lecture period (50 min) is close to 1 microcentury.
Find the percentage difference from the approximation? Answered by Stephen La Rocque. 





Percentage change 
20070813 

From Karen: I need a formula for calculating percentages in Excel. For example, we =
sold 4 units of an item one month, and 105 units the next. I need a =
formula to calculate the percentage increase in sales units. Also, if =
5251 were sold one month and 651 the next, what is the formula for =
calculating the percentage difference? Please help, thank you. Answered by Penny Nom. 





Simplifying an algebraic fraction expression 
20070725 

From Jessica: How do I simplify b/(b^{2}25) + 5/(b+5)  6/b? Answered by Stephen La Rocque. 





A statistical difference 
20070703 

From a student: I am writing a paper for a grad class in which I am comparing achievement levels of boys and girls. I have data that shows the average marks for girls and boys in each grade 12 subject for the entire province.
My prof want me to show there is a statistical difference. What do I have to do to show this? I don't have access to the raw data, so don't know the SD. Is there anything I can do mathematically with the data that I have? (I can determine n for each set of data, it ranges between 2400 and about 13000 for each subject area.) Answered by Chris Fisher and Harley Weston. 





Simplifying complex denominators 
20070621 

From Krys: How do I simplify completely?
((4+i ) / (3+i ))  ((2i ) / (5i )) Answered by Stephen La Rocque. 





What is the 100th term? 
20070615 

From George: I have the sequence
50,120,235,406,644
the 1st difference is 70,115,171,238
the 2nd difference is 45,56,67
the 3rd difference is 11,11
i used the a*n^3+b*n^2+c*n+d rule but the a turns out to be a decimal
because 11/6 is 1.833333333 and so i cant find the formula for the 100th term
term. Answered by Penny Nom. 





The difference between two dice 
20070602 

From smiley: Two standards dice are rolled. Determine the probability
that the difference between the two numbers on the dice is 2 Answered by Penny Nom. 





Percent difference 
20070517 

From Carolyn: What is the % difference between these two numbers 211373 & 185420 Answered by Gabriel Potter, Penny Nom and Steve La Rocque. 





Using the "difference of squares" formula how do I compute 27 * 33? 
20070402 

From Sarah: Using the "difference of squares" formula how do I compute 27 * 33? Answered by Penny Nom. 





The percentage difference between 64.24% and 74.24% 
20070303 

From M: What is the percentage difference between 64.24% and 74.24%? Answered by Stephen La Rocque and Penny Nom. 





Factoring polynomials 
20070214 

From Joe: I am in the eighth grade, and we are learning the equivalent of Algebra 2. I have no ides how to factor (x2)(x^21)6x6 You help is most aprreciated. Thank you! Joe Answered by Stephen La Rocque. 





Find the next 3 terms of the sequence 
20070207 

From rose: find the next 3 terms of the sequence 2,3,9,23,48,87 Answered by Penny Nom. 





Factoring m^49^n 
20061207 

From Josh: I can not figure out how to completely factor m^49^n. Answered by Penny Nom. 





(a^(1/3) – b^(1/3)) ( a^(2/3) + a^(1/3)b^(1/3) + b^(2/3)) 
20061024 

From Julie: (a^{1/3} – b^{1/3}) ( a^{2/3} + a^{1/3}b^{1/3} + b^{2/3}) Answered by Haley Ess. 





Percentage differences 
20061023 

From Michael: how do I calculate the percentage difference of a certain box size. for example. How much percent smaller is this box: 8.4mm x 6.3mm to this box: 9.35mm x 7mm Answered by Stephen La Rocque. 





Plotting percentage change 
20061011 

From Beckie: I have worked out a set of percentage differences which are all percentage decrease. Should i express them as a negative percentage as 20%? I also need to plot them on a graph and am not sure whether to just use the percentage difference as it is, in which case i get a positive gradient, or include a negative axis and plot them in this way, in which case i would get a negative gradient. I think the slope of the curve will be the same either way so it might not matter! Answered by Penny. 





Percentage Difference 
20060725 

From Sandra:
I have two numbers (1530 and 1315). How do I calculate the percentage difference.
For example: I have one loader that lifts 1530 lbs. and another loader that lifts 1315 lbs. I know the difference is 215 lbs. How much greater lift capacity does the loader that lifts 1530 lbs. have than the loader that lifts 1315 lbs.?
The formula that I used was:
1530  1315 = 215
215/1315 = .163498 or 16.3%
Is this correct?
Answered by Stephen La Rocque. 





Factor 
20060308 

From Brad: Factor:
x^{3} + 64m^{3} and 125p^{3}  q^{6} Answered by Penny Nom. 





3x^4  81 
20060102 

From Julio: How can I factor the following?:
3x^{4}  81 Answered by Penny Nom. 





A sum of 75 and a difference of 13 
20051030 

From Vicki: Find two numbers that have a difference of 13 AND A SUM OF 75? We need to learn about the formula or procedure. Answered by Penny Nom. 





1242, 826, 1034, 930, 1658 
20050831 

From Elizabeth: here is a math question my niece gave me, grade 7
1242, 826, 1034, 930, 1658
first day of school and this is what they give her no explanation Answered by Harley Weston. 





Difference in latitude 
20050405 

From Gretel: Assuming the the earth is a sphere of radius 6378 kilometers, what is the difference in latitude of two cities, one of which is 400 kilometers due north of the other? 500 kilometers? Answered by Penny Nom. 





The answer to a subtraction problem 
20050322 

From Libby: What is the name of a number that is the answer to a subtraction problem? Answered by Diane Hanson and Claude Tardif. 





"a" cubed minus "b" cubed 
20041202 

From Denise: "a"cubed minus "b"cubed equal (ab) times
("a"squared plus "ab" plus "b"squared)?
I know this is a formula, but why is it true? Answered by Penny. 





Factoring 
20040719 

From A student: Factor completely:
3x3  24y3
54x6 + 16y3
16xy  4x  4y  1
0.09x2  0.16y2 Answered by Penny Nom. 





3x squared  27 / x + 3 
20040504 

From Stef: 3x squared  27 / x + 3 Answered by Penny Nom. 





Some factoring problems 
20040415 

From KJ: Factor these:
x^{3}+125 > (x+5)^{3}
8x^{3}27 > (?)
x^{2}+36 > (x+6)^{2}
x^{4}5x^{2}+4 > (?) Answered by Penny Nom. 





Percent difference 
20040410 

From A parent: For a school science project, my son Alex is taking measurements of plant growth at regular intervals. As part of the data, he must provide the maximum percent difference observed in the categories his team has identified.
So, for example he has six plants with four measurements each. (He has more, but I'll keep it simple) For the first plant he measured 2mm, 2.4mm, 2.9mm, and 3.2mm. For the 2nd, 3rd, and 4th plants, he has similar numbers. Is there a way to calculate the maximum percent difference between any two plants in his measurements during the project? Doing it for each combination would be tedious. Answered by Penny Nom. 





Differences in percentages 
20040406 

From Jose:
Question:
You have two groups:
Group A has 10 people and 2 are Chinese
Group B has 12 people and 3 are Chinese
In terms of percentages what is the difference in Chinese between the two groups? In other words which group has the biggest percentage of Chinese and why?
Answered by Penny Nom. 





Percentage difference 
20040328 

From Someone: what is the percentage difference between 157 to 251 Answered by Penny Nom. 





Sums and differences 
20040210 

From David: The sum of two whole numbers is 63. The difference between the numbers is 10. Find all the possible pairs. Answered by Claude Tardif and Penny Nom. 





Difference of squares 
20031124 

From Susie:
Factor assuming that n is a positive #
Problem: (I will give it to you in words beacuse I don't know how to do exponents on the computer.)
Fortyfive r to the 2n power minus five s to the 4n power.
I was hoping you could walk me through it not just give me the answer.
Answered by Penny Nom. 





The 4th difference 
20031117 

From Jack: If i had a sequence which was the same at the 4th difference, aka difference
to the 4th, like:
1 5 14 30 56 96
(sequence)
4 9 16 26 40
5 7 10 14
2 3 4
1 1
then what would be the set formulars to find out a, b, c, d, and e
as i know the equation has to be an^{4}+bn^{3}+cn^{2}+dn+e Answered by Penny Nom. 





Is 3/5 CLOSEST to 0, 1/2 or 1? 
20030709 

From A student: I would like to know is 3/5 CLOSEST to 0, 1/2 or 1. And can 3/10 go either way as to be closest to 0 or 1/2. Answered by Penny Nom. 





The sum of two numbers is 5 and their difference is 
20030616 

From Akhil: The sum of two numbers is 5 and their difference is 11. What is the product of the two numbers? Answered by Penny Nom. 





Finite differences 
20030210 

From Jenny:
I need to find a formula that will work with any number. I am finding the volume of a 3d cross shape. Here are my results so far:
Term Number 0 1 2 3 4 5
nth term 1 7 25 63 129 231
1rst diff 6 18 38 66 102
2nd diff 12 20 28 36
3rd diff 8 8 8
I can't seem to find a formula that will work with any number. Any help would be much appreciated. Answered by Penny Nom. 





Factoring 
20021211 

From Larry: Question:
how do u factor trinonmials
EX: X^{ 3} + Y^{ 3}
X^{ 3}  8Y^{ 3}
8X^{ 2}  72
64A^{ 3}  125B^{ 6} Answered by Penny Nom. 





Percentage 
20020720 

From Sally: If 20% of 100 is 80, then why is the percentage difference between 80 and 100 25%. Answered by Penny Nom. 





Percentage difference 
20020308 

From Tedd: Can you give me the formulas for calculating percentage differences between two numbers? For example: if the first number is 10 and the second number is 15, then the second number is 50% larger than the first number. However, the formula to calculate that percentage won't work if the first number is greater than the second number as in the following example: The first number is 15 and the second number is 10, with the second number being 33.3% less than the first number. Or maybe I'm mistaken and the same formula will work in both situations. Answered by Penny Nom. 





Successive differences 
20020120 

From Linsey: what is the rule for working out the formula for a sequence with three lines of difference? eg.
1, 3, 7, 15, 29
1st line differences: 2, 4, 8, 14
2nd line differences: 2, 4, 6
3rd line differences: 2, 2 Answered by Penny Nom. 





Some algebra 
20011015 

From James: I cannot figure these out I was wondering if you could help me? I have no one to answer my questions.  (7x^{2} – 3yz)^{2} – (7x^{2} + 3yz)^{2}
 Use Pascal’s triangle to expand (2x – y)^{4}
 8x^{3} y  x^{3} y^{4}
 (m + 3n)^{2} – 144
 12x^{4} y – 16x^{3} y^{2} – 60x^{2} y^{3}
 p^{3} q^{2} – 9p^{3} + 27q^{2} – 243
Answered by Peny Nom. 





Finite differences 
20011008 

From Murray: My name is Murray and I am a 10th grade student. Me and my friend have recently discovered and proved a theorem of a relitively advanced nature. It is that the the nth difference of an nth degree equation = n! times the coefficient of the highest power. One of my teachers said this theorem is part finite and that she thinks she has seen it before, but she does not remember what it is called, at what level it is taught, who discovered it or when it was invented. I would greatly appretiate answers to any of these questions. Answered by Chris Fisher. 





Difference of Squares 
20010222 

From BrunoPierre: I noticed the other day that if you substract two consecutive squared positive numbers, you end up with the same result as if you add up the two numbers. Ex. 5 and 6 (2 consecutive positive numbers) 5^{2} = 25 6^{2} = 36 36  25 = 11 (Substraction of the squared numbers) 5 + 6 = 11 (Sum of the numbers) A more algebric view: a^{2}  b^{2} = a + b where a and b are consecutive positive positive numbers. (b = a + 1) I wondered if this rule had a name, and who discovered it. Answered by Penny Nom. 





Difference of squares 
20010220 

From Janna: Hi! I was just wondering how you would factor x^{2}  9y^{2}. Answered by Harley Weston. 





Factoring (uv)^{3}+vu 
20001215 

From A parent: I am a middle school teacher and a parent. I am snowed in and trying to help my 9th grader get ready for 9 weeks exams. I have tried to factor this problem to no avail. (uv)^3+vu. I have the answer but I need to know how it is done. Answered by Penny Nom. 





Factoring ^6 
20000103 

From Athena:
my name is Athena and I have a question on factoring: how would you figure this out: (x^{6}y^{6}) and (x^{6}+y^{6}) Answered by Penny Nom. 





The greatest possible difference 
19990917 

From Denea Hugunin: Use each of the digits 1 to 5 once to make a 2 digit number and a three digit number that the greatest possible difference. Answered by Penny Nom. 





A difference of squares problem. 
19990724 

From Michael and Stephanie Bixler: If you have the equation x= n^{2}  m^{2} (ie 40= 7^{2}3^{2}= 499) x must = a positive number 1) which squared numbers work as n and m 2) how does it work 3) if my teacher gave me the number for x; how could I figure out this problem Answered by Harley Weston. 





Introductory Algebra 
19990519 

From Pat: (2 + sq. root of 3) x (2  sq. root of 3) = 1 Please show me the work. Answered by Harley Weston. 





Factoring 
19990330 

From Maggie Stephens: I don't know anything about factoring would you plese help me. 3x^{4}  48 54x^{6} + 16y^{3} 1258x^{3} 12x^{2}  36x + 27 9  81x^{2} a^{3} + b^{3}c^{3} I would greatly appreciate any help you can give me thanks. Answered by Jack LeSage. 





Factoring 
19990308 

From L. Sivad: Question: m^{2}+6m+9n^{2} Answered by Penny Nom. 





Finding a rule for a sequence 
19990217 

From Lindsey Masters: I'm doing a maths investigation and i have a sequence which goes: 13,16,25,32,45,56,73. Our teacher told us we have to find a rule by looking at the differences of the terms until we find a constant. The first differences are: 3,9,7,13,11,17. The differences of these are: ...... Please could you tell me how to work it out so that I could work out the rules of similar sequences. Answered by Penny Nom. 





What's the next term? 
19981112 

From Ilia: What the formula and explonation for formula for next patterns: 1) 1, 4, 10, 20, 35, 56, 84,... 2) 0, 6, 30, 90, 210, 420,... Thanks! Answered by Penny Nom. 





Difference of squares 
19980623 

From Kristen Smelsky: Solve the following using a difference of squares: 4x(squared) minus 4xy plus y(squared) minus m(squared) plus 2m minus 1 Answered by Penny Nom. 

