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(a-b)^2 Expansion and Visualisation

Factorize: p...

Question

Factorize: $p^{2} + 10 p + 25$

(p + 5)^{2}

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(p - 5)^{2}

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(2 p + 5)^{2}

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(2 p - 5)^{2}

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Solution

The correct option is A: $(p + 5)^{2}$
We have, $p^{2} + 10 p + 25$
$= p^{2} + 5 p + 5 p + 25$
$= p (p + 5) + 5 (p + 25)$
$= (p + 5) (p + 5)$
$= (p + 5)^{2}$
Alternate method:
$p^{2} + 10 p + 25$
$= p^{2} + (2 \times p \times 5) + 5^{2}$ [Using the identity, $a^{2} + 2 a b + b^{2} = (a + b)^{2}$ ]
$= (p + 5)^{2}$

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