f(x)=(2x+3)(x-2) and g(x)=2x^2-16. Find g(x)-f(x)
$$\begin{array}{rlll} g(x)-f(x)&=&2x^2-16-[(2x+3)(x-2)]&\\\\ &=&2x^2-16-[(2x(x-2)+3(x-2)]&\\\\ &=&2x^2-16-[2x^2-4x+3x-6]&\\\\ &=&2x^2-16-[2x^2-x-6]&\\\\ &=&2x^2-16-2x^2+x+6&\\\\ &=&x-10&\\\\ \end{array}$$
