My workbook says the answer to this:
$a^2 + ab - b^2 - \frac {a^3 - 2b^3}{a - 2b} $
is:
$- \frac {a^2b + 3ab^2 - 4b^3}{a - 2b}$
I am continually getting this answer though:
$\frac {-a^2b - 3ab^2}{a - 2b}$
What am I doing wrong here? Is there somewhere I should be multiplying by -1?
My work: $a^2 + ab - b^2 - \frac {a^3 - 2b^3}{a - 2b} $
$= \frac {a^2(a-2b)+ab(a-2b)-b^2(a-2b)-a^3-2b^3}{a-2b}$
$= \frac {a^3-2a^2b+a^2b-2ab^2-ab^2+2b^3-a^3-2b^3}{a-2b}$
$= \frac {-a^2b - 3ab^2}{a - 2b}$
Your mistake is at the far right of your numerator: you did not distribute the negative sign. Your answer should be (correction in red) $$\displaystyle\frac{a^{2}(a-2b)+ab(a-2b)-b^{2}(a-2b)\color{red}-(a^{3}-2b^{3})}{a-2b}$$