Factorize the following using appropriate identities: $9 x^{2} + 6 x y + y^{2}$ .

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Solution

Factorize the given polynomial
$9 x^{2} + 6 x y + y^{2} = {(3 x)}^{2} + 2 \times 3 x \times y + {(y)}^{2}$
Use the identity ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$
$9 x^{2} + 6 x y + y^{2} = {(3 x + y)}^{2}$
Hence, the factorized form of $9 x^{2} + 6 x y + y^{2}$ is $(3 x + y) (3 x + y)$

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