Question

If `f(x) = 2x^2 - 4x - 3` and `g(x) = (x - 4)(x + 4)`, find `f(x) - g(x).`

Answer 1

`\large\boxed{f(x)-g(x)=x^2-4x+13}`

Explanation:

`f(x)=2x^2-4x-3\\\\g(x)=(x-4)(x+4)=x^2-4^2=x^2-16\qquad\text{used}\ a^2-b^2=(a-b)(a+b)\\\\f(x)-g(x)=(2x^2-4x-3)-(x^2-16)\\\\=2x^2-4x-3-x^2-(-16)\\\\=2x^2-4x-3-x^2+16\qquad\text{combine like terms}\\\\=(2x^2-x^2)-4x+(-3+16)\\\\=x^2-4x+13`