Question

combining functions by subtraction
the areas of two rectangles can be represented by the functions shown.
which function represents the difference in the areas, $h(x)=f(x)-g(x)$?
$f(x)=5x^{2}-2x + 1$
$h(x)=4x^{2}-4x - 11$
$h(x)=4x^{2}-4x + 11$
$h(x)=-4x^{2}+4x + 11$
$h(x)=4x^{2}-4x - 9$
$g(x)=x^{2}+2x - 10

Explanation:

Step1: Write the subtraction expression

$h(x)=(5x^{2}-2x + 1)-(x^{2}+2x - 10)$

Step2: Distribute the negative sign

$h(x)=5x^{2}-2x + 1 - x^{2}-2x + 10$

Step3: Combine like - terms

$h(x)=(5x^{2}-x^{2})+(-2x-2x)+(1 + 10)$
$h(x)=4x^{2}-4x + 11$

Answer:

$h(x)=4x^{2}-4x + 11$