Question

Multiply (in horizontal and vertical arrangement):

(5) (m + n) (m − n)

Answer 1

(m + n) (m − n)
Horizontal arrangement:
= (m + n) × m − (m + n) × n
= m × m + n × m − m × n − n
= m² + nm − mn − n²
= m² − n²

Vertical arrangement:
$\begin{array}{c}\begin{array}{ccccc}& & m& +& n\end{array}\\ \begin{array}{ccccc}& \times & m& -& n\end{array}\\ \overline{\begin{array}{ccccc}& & -mn& -& n^2\end{array}}\\ \begin{array}{ccccc}+m^2& +& mn& & \end{array}\\ \underline{\overline{\begin{array}{ccccc}{m}^2& +& 0& -& n^2\end{array}}}\end{array}$