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Factorisation Using Algebraic Identities

Factorise: ...

Question

Factorise: $169 x^{2} - 144 y^{2}$

(13 x - 11 y) (13 x + 11 y)

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(14 x - 13 y) (14 x + 13 y)

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(13 x - 12 y) (13 x + 12 y)

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(12 x - 13 y) (12 x + 13 y)

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Solution

The correct option is C $(13 x - 12 y) (13 x + 12 y)$
Given, $169 x^{2} - 144 y^{2}$
$= {(13 x)}^{2} - {(12 y)}^{2}$
$= (13 x - 12 y) (13 x + 12 y)$ ... $[∵ a^{2} - b^{2} = (a - b) (a + b)]$

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