Question

Multiply (in horizontal and vertical arrangement):

(8) (3p² + q) (4p − 2q)

Answer 1

(3p² + q) (4p − 2q)
Horizontal arrangement:
= (3p² + q) × 4p − (3p² + q) × 2q
= 3p² × 4p + q × 4p − 3p² × 2q − q × 2q
= 12p³ + 4pq − 6p²q − 2q²

Vertical arrangement:
$\begin{array}{c}\begin{array}{ccccccc}& & & & 3p^2& +& q\end{array}\\ \begin{array}{ccccccc}& & & \times & 4p& -& 2q\end{array}\\ \overline{\begin{array}{ccccccc}& & & & -6p^{2}q& -& 2q^2\end{array}}\\ \begin{array}{ccccccc}+12p^3& +& 4pq& & & & \end{array}\\ \underline{\overline{\begin{array}{ccccccc}12p^3& +& 4pq& -& 6p^{2}q& -& 2q^2\end{array}}}\end{array}$