Name: Melissa

Who is asking: Student Level: Middle

Question:
Alright, lets say you are multiplying (-2b+3)(-b-1) and you are using "FOIL" first you would get : 2b2+2b-3b-3 then you add like-terms. when multiplying,if the bases are the same, add the exponents...does the same thing apply when you are adding the results of the multiplication even though it's addition?

would the answer be 2b3-3b-3 or would it be 2b2-b-3?

please help!

Hi Melissa,

Try it with some numbers. Using * for multiplication,

3*32 = 3*9 = 27 and using the rules of exponents 3*32 = 31+2 = 33 = 27

For addition

3 + 32 = 3 + 9 = 12 which is not the same as 33

Your second answer is correct

2b2+2b-3b-3 = 2b2-b-3

By the way I don't like the use of the FOIL mnemonic to do this problem. It fails as soon as you extend this problem one step to (-2b+3)(b2-b-1). Just think about what you've learned when you multiply in base 10. Suppose you are multiplying 17 x 28. 

     17
     28
     --
    136
    34
    ---
    476

If you think of the steps in performing this multiplication, what you did was

8x7 = 56
8x10 = 80
20x7 = 140
20x10 = 200 and then you added to get 476. You use "columns" so that we don't have to write all the zeros and you "carry" along the way but what you are actually doing is 17x20 =
(7+10)x(8+20)=
56 + 80 + 140 + 200 =
476

If one of the factors is 3 digits then 

     17
    128
     --
    136
    34
   17
   ----
   2176
or 17x20 =
(7+10)x(8+20+100)=
56 + 80 + 140 + 200 + 700 + 1000=
2176 In a simiar fashion (-2b+3)(b2-b-1)=
-2b3 + 3b2 +2b2 -3b +2b - 3=
-2b3 + 5b2 -b -3 Cheers,
Penny
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