Prove that \((6p) × (4c) × (p + 2)\) \(=\) 24\(p^{2} c\) \(+\) 48\(pc\).
Proof:
\((6p) × (4c)\) \(=\)
\(\times\) \((p + 2)\)
The above product is expanded using .
The first term is expanded as follows:
24\(pc\)\(\times\) \(p\) \(=\) 24\(p^{1+1} c\) [By ]
\(=\) 24\(p^{2} c\)
The second term is expanded as follows:
24\(pc\)\(\times\) \(2\) \(=\) 24 \(\times 2\) \(p \times c\)
\(=\) \(pc\)
Combine the terms.
\((6p) × (4c) × (p + 2)\) \(=\) 24\(p^{2} c\) + \(pc\).
Hence, proved.