Solve: p^2+ 6p - 16 - Vidyadip

Question

Solve:
$p^2+ 6p - 16$

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Answer

$p^2+ 6p - 16$
$\text{p}^2+6\text{p}+\Big(\frac{6}{2}\Big)^2-\Big(\frac{6}{2}\Big)^2-16$ $\Big[$Adding and suobtrating $\Big(\frac{6}{2}\Big)^2,$ that is $3^2$$\Big]$
$= p^2+ 6p + 3^2- 9 - 16$
$= (p - 3)^2- 25$ [completing the square]
$= (p + 3)^2- 5^2$
$= [(p + 3) - 5][(p + 3) + 5]$
$= (p + 3 - 5)(p + 3 + 5)$
$= (p - 2)(p + 8)$

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