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The factors of the expression $9 x 2 + 6 x y + y 2$ using appropriate identity is:

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(x + y) (x + y)

(2x + y) (2x + y)

(3x + y) (3x + y)

(4x + y) (4x + y)

answer is C.

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Detailed Solution

Given:

9 x 2 + 6 x y + y 2

Let us rewrite the given expression as:

= (3 x) 2 + (2 × 3 x × y) + y 2

Comparing the given expression with a² + 2ab + b², we observe that a = 3x & b = y.
Again by sing algebraic identity, (a + b)² = a² + 2ab + b² we get:

9 x 2 + 6 x y + y 2 = (3 x + y) 2

= (3 x + y) (3 x + y)

Hence, 9x² + 6xy + y² = (3x + y) (3x + y)
Therefore, the correct option is 3.

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