Factorise: $36 x^{2} - 81 y^{2}$

9 (6 x - 9 y) (6 x + 9 y)

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3 (6 x - 9 y) (6 x + 9 y)

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9 (2 x - 3 y) (2 x + 3 y)

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

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Solution

The correct option is C. $9 (2 x - 3 y) (2 x + 3 y)$
Given expression is $36 x^{2} - 81 y^{2}$
We can factorise the given expression by rewriting it and combining common terms.
$36 x^{2} - 81 y^{2} = {(6 x)}^{2} - {(9 y)}^{2}$
$= (6 x - 9 y) (6 x + 9 y)$ $[∵ a^{2} - b^{2} = (a - b) (a + b)]$
$= 3 (2 x - 3 y) \times 3 (2 x + 3 y)$
$= 9 (2 x - 3 y) (2 x + 3 y)$

Therefore, $36 x^{2} - 81 y^{2} = 9 (2 x - 3 y) (2 x + 3 y)$

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Similar questions

Factorization:

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

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

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

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