Question 942507
find:
{{{(g*w)(x)}}} and {{{(w*g)(x)}}} for {{{g(x) =3x-2}}} and {{{w(x) =x^2-3x+4}}}

first recall that {{{(g*w)(x)=(w*g)(x)}}} (commutative property of multiplication)

so, {{{(g*w)(x)=(3x-2)(x^2-3x+4)}}}

 {{{(g*w)(x)=3x(x^2-3x+4)-2(x^2-3x+4)}}}

{{{(g*w)(x)=(3x^3-9x^2+12x)-(2x^2-6x+8)}}}

{{{(g*w)(x)=3x^3-9x^2+12x-2x^2+6x-8}}}

{{{(g*w)(x)=3x^3-11x^2+18x-8}}}

then, also {{{(w*g)(x)=3x^3-11x^2+18x-8}}}