Question

Multiply (in horizontal and vertical arrangement):

(12) (3p − 5q) (3p + 5q)

Answer 1

(3p − 5q) (3p + 5q)
Horizontal arrangement:
= (3p − 5q) × 3p + (3p − 5q) × 5q
= 3p × 3p − 5q × 3p + 3p × 5q − 5q × 5q
= 9p² − 15qp + 15pq − 25q²
= 9p² − 25q²

Vertical arrangement:
$\begin{array}{c}\begin{array}{cccccc}& & & 3p& -& 5q\end{array}\\ \begin{array}{cccccc}& & \times & 3p& +& 5q\end{array}\\ \overline{\begin{array}{cccccc}& & & 15pq& -& 25q^2\end{array}}\\ \begin{array}{cccccc}+& 9p^2& -& 15pq& & \end{array}\\ \underline{\overline{\begin{array}{cccccc}& 9p^2& +& 0pq& -& 25p^2\end{array}}}\end{array}$