Answer
a. $-x^{2}+12x-12$, b. $9x^{2}+4x+6$
Work Step by Step
We are given that $f(x)=4x^{2}+8x-3$ and $g(x)=-5x^{2}+4x-9$.
We know that $(f+g)(x)=f(x)+g(x)$ and $(f-g)(x)=f(x)-g(x)$.
Therefore:
$(f+g)(x)=(4x^{2}+8x-3)+(-5x^{2}+4x-9)=4x^{2}-5x^{2}+8x+4x-3-9=-x^{2}+12x-12$.
$(f-g)(x)= (4x^{2}+8x-3)-(-5x^{2}+4x-9)=4x^{2}+5x^{2}+8x-4x-3+9=9x^{2}+4x+6$