Question

Given that Q(x)=2x^2 +5x-3 find and simplify Q(a+h)-Q(a-h)

Answer 1

`Q(a+h)-Q(a-h)=8ah+10h`

Explanation:

We are given the function:

`Q(x)=2x^2+5x-3`

And we want to find and simplify:

`Q(a+h)-Q(a-h)`

Substitute:

`=[2(a+h)^2+5(a+h)-3]-[2(a-h)^2+5(a-h)-3]`

Expand:

`\displaystyle =[2(a^2+2ah+h^2)+5a+5h-3]-[2(a^2-2ah+h^2)+5a-5h-3]`

Distribute:

`=[2a^2+4ah+2h^2+5a+5h-3]-[2a^2-4ah+h^2+5a-5h-3]`

Distribute:

`=(2a^2+4ah+2h^2+5a+5h-3)+(-2a^2+4ah-2h^2-5a+5h+3)`

Rewrite:

`=(2a^2-2a^2)+(4ah+4ah)+(2h^2-2h^2)+(5a-5a)+(5h+5h)+(-3+3)`

Combine like terms:

`=8ah+10h`

Hence:

`Q(a+h)-Q(a-h)=8ah+10h`