Factorize the given expression:

$9 (2 x - 3 y)^{2} - 12 (2 x - 3 y) (2 x + 3 y) + 4 (2 x + 3 y)^{2}$

$(2 x - 15 y)^{3}$

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$(2 x + 15 y)^{2}$

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$(2 x + 15 y)^{3}$

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$(2 x - 15 y)^{2}$

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Solution

The correct option is D
$(2 x - 15 y)^{2}$

$9 (2 x - 3 y)^{2} - 12 (2 x - 3 y) (2 x + 3 y) + 4 (2 x + 3 y)^{2}$

Let $(2 x - 3 y) = a$ and $(2 x + 3 y) = b$

$\Rightarrow 9 a^{2} - 12 a b + 4 b^{2}$

$= 9 a^{2} - 6 a b - 6 a b + 4 b^{2}$

$= 3 a (3 a - 2 b) - 2 b (3 a - 2 b)$

$= (3 a - 2 b) (3 a - 2 b)$

$= (3 a - 2 b)^{2}$

Substituting values of a and b,

$\Rightarrow (3 (2 x - 3 y) - 2 (2 x + 3 y))^{2}$

$= (6 x - 9 y - 4 x - 6 y)^{2}$

$= (2 x - 15 y)^{2}$

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Similar questions

Factorize the given expression:

$9 (2 x - 3 y)^{2} - 12 (2 x - 3 y) (2 x + 3 y) + 4 (2 x + 3 y)^{2}$

Factorization:

$9 (2 x - 3 y)^{2} - 12 (2 x - 3 y) (2 x + 3 y) + 4 (2 x + 3 y)^{2}$

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

(2 x + 3 y)^{2}

(2 x - 3 y)^{2}

(2 x + 3 y) (2 x - 3 y)

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

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