Factorize the following algebraic expression:

$36 a^{2} + 36 a + 9$

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Solution

Given: $36 a^{2} + 36 a + 9$

$= 9 (4 a^{2} + 4 a + 1)$

$= 9 [(2 a)^{2} + 2 \times 2 a \times 1 + (1)^{2}]$

Using the formula, $(x + y)^{2} = x^{2} + 2 x y + y^{2}$

$= 9 (2 a + 1)^{2}$

$= 9 (2 a + 1) (2 a + 1)$

$∴ 36 a^{2} + 36 a + 9 = 9 (2 a + 1) (2 a + 1)$

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