







How many cubes are in a 3x3x3 cube? 
20190624 

From Darren: Dear Sir/Madam,
How many cubes of different sizes (eg. 1x1x1, 2x2x2, 3x3x3) are there in total in say,
a 3x3x3 cube? I have trouble figuring this out.
Yours faithfully,
Darren 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. 





Five cubes 
20140115 

From Bob: Rick has five cubes. When he arranges them from smallest to largest, the difference between the heights of any two neighbouring cubes is 2 cm. The largest cube is as high as a tower built from the two smallest cubes. How high is a tower built from all five cubes? Answered by Penny Nom. 





Squares and cubes 
20130802 

From Sandra: What whole number equals 25 when it is squared and 125 when it is cubed? Answered by Penny Nom. 





a cubeb cubea+b= ? 
20130616 

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





Two cubes 
20120904 

From alexis: a cube has one face that is equal to the total surface area of another cube. Find the ratio of their volumes Answered by Penny Nom. 





Three metallic cubes 
20120513 

From Pragun: Three metallic cubes whose edges are in the ratio 3:4:5 are melt to form a single cube whose diagonal is 12*square root of 3. What are lengths of the edges(in cm) of the three cubes Answered by Penny Nom. 





A pattern is built with cubes. 
20110208 

From e: A pattern is built with cubes.
The first item is 1 cube.
The second item is a block of 8 cubes.
The third item is a block of 27 cubes.
If the pattern is continued, how many cubes are needed for the fourth and fifth? 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. 





1^3 + 2^3 + 3^3 +4^3 ... n^3 = ? 
20100129 

From ireimaima: Hi..
Can u please help me with this question..
I find that when i test eg: n=2 for n (n+1) /4,
it seems that it does not giving me the right answer of 1^3 + 2^3 = 9
but 3/2... i'm confuse..can u please help me..thanks so much
Prove that:
1^3 + 2^3 + 3^3 +4^3
..n^3 = n (n+1) /4 Answered by Penny Nom. 





Cubes and squares 
20090916 

From Stanley: What is a three consecutive digit number like 5,6,7 , which is two less than a cube and two more than a square? Answered by Robert Dawson. 





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. 





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. 





A cubic equation 
20080825 

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





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. 





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. 





How many cubes have one face painted red? 
20071127 

From Ashutosh: A rectangular block measuring 10 units by 8 units by 6 units is made up of cubes measuring 1 unit on a side. The base of the block is 10 units by 8 units. The outside of the block other than the base is painted red. How many of the unit cubes have exactly one face painted red? Answered by Stephen La Rocque and Penny Nom. 





Cubes 
20070921 

From Yvonne: The numbers 756 and 72, expressed as products of prime factors, are 756 = 2² x 3³ x 7 and 72 = 2³ x 3²
Use these result to find,
the smallest integer, x, such that 756x is a perfect cube. Answered by Penny Nom. 





Find all numbers which are both squares and cubes 
20070730 

From Arul: what is the easiest way to find the number which is both a square and a cube?
the numbers i know are 64 and 729 which is both a sqr and a cube.
i took long time to solve this.. is there any easier way? Answered by Steve La Rocque. 





A trillion sugar cubes 
20061110 

From Leeza: How many dump trucks (I believe the standard bed size is 16'L x 8'W x 4'D) would it take to hold one trillion sugar cubes (which I believe are approximately 2cm in L, W and D)? 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. 





How many of these cubes have no wax of them? 
20060310 

From Iban: cube cheese is 4cm wide, 4cm long, 4cm high. three faces of the cube meet in the corner covers thin layers of wax. The cheese is then cut two, then cut 64 small cubes, which is the length 1cm.
How many of these cubes have no wax of them? 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" 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. 





Slicing cubes 
20041123 

From Anthony: You are working with a power saw and wish to cut a wooden cube 3inches on aside into 27 1inch cubes. You can do this by making six cuts through the cube keeping the pieces together in the cube shape. Can you reduce the number of necessary cuts by rearranging the pieces after each cut? Answered by Chris Fisher. 





Factoring 
20040719 

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





Factoring 
20040427 

From Bipin: FACTORISE:
a to the power of 6 + b to the power of 6 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. 





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. 





Factor completely 
20021121 

From Shelley: these two questions are to be factored completely but i have no idea how to factor them  (x4y)^{ 2}  3(x4y)  4
 x^{ 6} + y^{ 6}
Answered by Penny Nom. 





Two cubes 
20020712 

From Vanessa: The edges of a cube are 50% as long as the edges of another cube. What percent of the volume of the larger cube is the volume of the smaller cube? Answered by Peny Nom. 





24x^4 + 3x 
20020318 

From gary: 24x^{ 4} + 3x Answered by Penny Nom. 





The number of hidden cubes 
20020205 

From Katie: This problem is about finding the number of cubes visible and hidden in a cube.
In a cube that is 3x3, 19 cubes can be seen. 8 are hidden. In a cube that is 4x4, 37 cubes can be seen. 27 are hidden. In a cube that is 5x5, 61 cubes can be seen. 64 are hidden. In a cube that is 6x6, 91 cubes can be seen. 125 are hidden. The question is: Explain how you could find the number of small cubes that are visible and hidden in a cube of any size. Answered by Paul Betts and 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 Pascals 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. 





The sum of the cubes is the square of the sum 
20001010 

From Otoniel: Without using mathematical induction, or any other method discovered after 1010 a.d. , prove that the sum of i^{3}, (where i, is the index of summation) from one to, n, is equal to ((n*(n+1))/2)^{2} 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. 





towers of cubes 
19991005 

From Sanker: I need help to solve this Rules for bulding towers of cubes rule 1  The number of cubes on the bottom layer is always one less than the number of squares on the grid  rule 2  Each new layer is made with one cube less than the layer underneath it.   Investigate how many different arrangements there are of 4 cubes on top of 5 cubes on a two by three grid
 investigate the number of different arrangements of six cubes on top of seven cubes on a two by four grid
 investigate the relation between the number of arrangements of cubes and the size of the grid
 when there are two layers of cubes
 when there are more than two layers of cubes
Answered by Walter Whiteley. 





The sum of the cubes is the square of the sum 
19990825 

From Bernard Yuen: How to prove 1^{3} + 2^{3} + 3^{3} + 4^{3} + ... n^{3} is equal to (1+2+3+...n)^{2}? (for n is positive integer) 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. 





Patterns 
19990107 

From Melis Kalay: I'm confused about questions like these: 1. 2by2by2 cube: If this cube was painted blue on the outside,  how many cubes would have 3 blue faces
 2 blue faces
 1 blue face
 0 blue faces
Answered by Jack LeSage and Penny Nom. 

