Find the coefficients of $( a + b x ) \cdot ( c + d x )$ in terms of $a , b , c , d$, and explain why $f ( x ) \cdot g ( x ) = g ( x ) \cdot f ( x )$ for all linear polynomials $f ( x )$ and $g ( x )$.
Find the coefficients of $( a + b x ) \cdot ( c + d x )$ in terms of $a , b , c , d$, and explain why $f ( x ) \cdot g ( x ) = g ( x ) \cdot f ( x )$ for all linear polynomials $f ( x )$ and $g ( x )$.