Question 158078
Let {{{w=a-2b}}} and {{{z=a-b}}} (note: {{{-z=b-a}}}). So this means that the expression 



{{{(a-2b)(a+3b)(b-a)-(4a+5b)(a-b)(a-2b)}}}



becomes



{{{w(a+3b)(-z)-(4a+5b)zw}}}



{{{-wz(a+3b)-wz(4a+5b)}}} Rearrange the terms.



{{{-wz(a+3b+4a+5b)}}} Factor out the GCF {{{-wz}}}



{{{-wz(5a+8b)}}} Combine like terms.



{{{-(a-2b)(a-b)(5a+8b)}}} Plug in {{{w=a-2b}}} and {{{z=a-b}}}



So {{{(a-2b)(a+3b)(b-a)-(4a+5b)(a-b)(a-2b)}}} factors to {{{-(a-2b)(a-b)(5a+8b)}}} (the order of the factors does not matter)




Note: the factor {{{-(a-b)}}} is equivalent to {{{b-a}}}