Question

Can someone please explain this 4x
`(4x^(2) -5x)- (4x^(2) -4x-8)`

the answer is -x+8 but I don't get why its +8 and not -8

Answer 1

Your first step of simplifying is to distribute the "–" or "–1" in front of the second set of parentheses through that second set of parentheses. The –1 must be distributed to every term in the second set:

`\begin{aligned}(4x^2-5x)-(4x^2-4x-8)&=(4x^2-5x)\boldsymbol{{}-1}(4x^2-4x-8)\\[0.5em]&=4x^2-5x\boldsymbol{{}-1(4x^2)-1(-4x)-1(-8)}\\[0.5em]&=4x^2-5x\boldsymbol{{}-4x^2+4x+8}\\[0.5em]&=-x+8\\\end{aligned}`

That's what changes the sign on every term in the second set of parentheses, making that –8 become +8.