Question 51881
For a problem like this, we multiply every term in the first polynomial by every term in the second, thus we should get nine terms when we're done...like this:
(a^2 + 2ab - b^2)(a^2 - 7ab + b^2)=
a^4 - 7a^3b + a^2b^2
+2a^3b - 14a^2b^2 + 2ab^3
-a^2b^2 + 7ab^3 - b^4
Now we combine like terms to get
a^4 - 5a^3b - 14a^2b^2 + 9ab^3 - b^4