Factorise:
$16 x^{4} - 81 y^{4}$

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

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

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

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

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Solution

The correct option is C $(4 x^{2} + 9 y^{2}) (2 x + 3 y) (2 x - 3 y)$
$16 x^{4} - 81 y^{4} = {(4 x^{2})}^{2} - {(9 y^{2})}^{2} = (4 x^{2} + 9 y^{2}) (4 x^{2} - 9 y^{2}) (∵ a^{2} - b^{2} = (a + b) (a - b)) = (4 x^{2} + 9 y^{2}) [{(2 x)}^{2} - {(3 y)}^{2}] = (4 x^{2} + 9 y^{2}) (2 x + 3 y) (2 x - 3 y)$

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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) (2 x - 3 y)

Simplify: $(2 x - 3 y) (2 x + 3 y)$

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