Are you sure the first term is not supposed to. be b^{2}(a**-**b) rather than b^{2}(a+b)?

If so, the answer is ** a**^{3}**-b**^{3}

Explanation:

If the first term is b^{2}(a**-**b), then the first step is to distribute the negative to the second and third terms so that the equation now becomes

b^{2}(a**-**b)-ab(b-a)-a^{2}(b-a)

Next, pull out the negatives of the (b-a) term in the second and third terms so the equation becomes

b^{2}(a**-**b)-(-1)ab(b-a)-(-1)a^{2}(b-a)

Next, multiply out the -1 and change it to

b^{2}(a-b)+ab(a-b)+a^{2}(a-b)

Next, factor out the (a-b) from all three terms and combine and the equation becomes

(a-b)(b^{2}+ab+a^{2})

Finally, rewrite that to what should like a familiar form

(a-b)(a^{2}+ab+b^{2})

That equation is the expansion of a^{3}-b^{3}

**So the answer is a**^{3}**-b**^{3}