Question

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

Answer 1

Answer:

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

Step-by-step 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:

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