This is the equation:
$(2a - 3b)^2 - (a+2b)^3 + 7a^2(6b - a)$
Here is what I tried:
$4a^2 - 12ab + 9b^2 -(a^3 + 6a^2b + 12ab^2 + 8b^3) + 42a^2b - 7a^3$
$4a^2 - 12ab + 9b^2 - a^3 - 6a^2b - 12ab^2 - 8b^3 + 42a^2b - 7a^3$
$4a^2 - 8a^3 - 8b^3 - 12ab + 9b^2 - 12ab^2 + 36a^2b$
$4a^2 - 8(a^3 + b^3) - 12ab + 9b^2 - 12ab^2 + 36a^2b$
$4a(a + 9ab - 3b) + 3b(3b - 4ab) - 8(a^3 + b^3)$
The answer is supposed to be:
$42ab^2 - 35b^3$
However I have no idea how to get to it, I've been trying to transform it into different ways and always end up at the same spot above.
Am I wrong in my method of factoring? Should I have done something totally different?
There is no need to evaluate the expression to see that it cannot match the given answer.
Because the answer is an homogeneous cubic polynomial in $a,b$, while the expression has quadratic terms which do not simplify.
But
$$(2a - 3b)^\color{red}3 - (a+2b)^3 + 7a^2(6b - a)=42ab^2-35b^3.$$