Factorize the following expression
$9 x^{2} + y^{2} + 1 - 6 x y + 6 x - 2 y$

(3 x - y + 1)^{2}

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(3 x - y + 1)^{3}

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(3 x - y - 1)^{2}

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None of these

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Solution

The correct option is B $(3 x - y + 1)^{2}$
$(3 x)^{2} + (y)^{2} + (1)^{2} - 2 (3 x) y + 2 (3 x) - 2 (y) (1)$

Using identity $= (A + B + C)^{2} = A^{2} + B^{2} + C^{2} + 2 A B + 2 B C + 2 C A$ ...........(i)

$9 x^{2} + y^{2} + 1 - 6 x y + 6 x - 2 y$

$= (3 x)^{2} + (- y)^{2} + (1)^{2} + 2 (3 x) (- y) + 2 (3 x) (1) + 2 (1) (- y)$

Comparing with........................(i), we get
$= (3 x - y + 1)^{2}$

Suggest Corrections

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