Question

What is `g(x+a)-g(x)` when `g(x)=-x^2-x`?

Answer 1

I got:
`g(x+a)-g(x)=-(x+a)^2-(x+a)-(-x^2-x)`

Explanation:

Let us use our constant `a`:
`g(x+a)-g(x)=color(red)(-(x+a)^2-(x+a))color(blue)(-x^2-x)`
Where:
Red = `g(x+a)`
Blue= `g(x)`

We can also rearrange to try to simplify it.

Answer 2

`g(x+a) -g(x) =-a(a+2x+1)`

Explanation:

`g(x)= -x^2-x :. g(x+a) = -(x+a)^2 -(x+a) = -(x^2+2ax+a^2)- (x+a) = -x^2 -2ax - a^2 -x -a :. g(x+a) -g(x) = -x^2 -2ax - a^2 -x -a - (-x^2-x) = cancel(-x^2) -2ax - a^2 cancel(-x) -a + cancelx^2+ cancel x = -a(a+2x+1)`[Ans]