SOLUTION: Simplify/Factor: (a-2b)(a+3b)(b-a)-(4a+5b)(a-b)(a-2b) the answer is (b-a)(a-2b)(5a+8b) I can definitely see the familiarities in the answer and question but i really don'

Algebra ->  Expressions-with-variables -> SOLUTION: Simplify/Factor: (a-2b)(a+3b)(b-a)-(4a+5b)(a-b)(a-2b) the answer is (b-a)(a-2b)(5a+8b) I can definitely see the familiarities in the answer and question but i really don'      Log On


   

Question 158078: Simplify/Factor:
(a-2b)(a+3b)(b-a)-(4a+5b)(a-b)(a-2b)
the answer is (b-a)(a-2b)(5a+8b)
I can definitely see the familiarities in the answer and question but i really don't know how the book arrived at that answer.
Found 2 solutions by jim_thompson5910, Earlsdon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let w=a-2b and z=a-b (note: -z=b-a). So this means that the expression


%28a-2b%29%28a%2B3b%29%28b-a%29-%284a%2B5b%29%28a-b%29%28a-2b%29


becomes


w%28a%2B3b%29%28-z%29-%284a%2B5b%29zw


-wz%28a%2B3b%29-wz%284a%2B5b%29 Rearrange the terms.


-wz%28a%2B3b%2B4a%2B5b%29 Factor out the GCF -wz


-wz%285a%2B8b%29 Combine like terms.


-%28a-2b%29%28a-b%29%285a%2B8b%29 Plug in w=a-2b and z=a-b


So %28a-2b%29%28a%2B3b%29%28b-a%29-%284a%2B5b%29%28a-b%29%28a-2b%29 factors to -%28a-2b%29%28a-b%29%285a%2B8b%29 (the order of the factors does not matter)



Note: the factor -%28a-b%29 is equivalent to b-a

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Try this!
Factor the indicated factors from both terms.
%28a-2b%29%28%28a%2B3b%29%28b-a%29-%284a%2B5b%29%28a-b%29%29 Now, %28a-b%29+=+-%28b-a%29 so make the substitution in the second term.
Factor the indicated factors from both terms and change the - to +
%28b-a%29%28a-2b%29%28highlight%28%28a%2B3b%29%2B%284a%2B5b%29%29%29 Perfom the indicated addition.
highlight%28%28b-a%29%28a-2b%29%285a%2B8b%29%29