Question

Prove the equation \((a - b) \times (a + b) = 2(a \times b)\).

Short answer

The expression \((a - b) \times (a + b) = a \times b + a \times b\)\( = 2(a \times b)\)is proved.

Step-by-step solution

Expand the equation.

Consider \((a - b) \times (a + b)\)

Simplify the equation.

\(\begin{array}{l}({\rm{a}} - {\rm{b}}) \times ({\rm{a}} + {\rm{b}}) = {\rm{a}} \times {\rm{b}} + {\rm{a}} \times {\rm{b}}\\({\rm{a}} - {\rm{b}}) \times ({\rm{a}} + {\rm{b}}) = 2({\rm{a}} \times {\rm{b}})\end{array}\)

Hence, the expression \((a - b) \times (a + b) = 2(a \times b)\) is proved.