Factorise: $225 x^{2} - 180 x y + {36 y}^{2}$

9 (2 x - 5 y) (2 x + 5 y)

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9 (5 x - 2 y) (5 x - 2 y)

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9 (5 x - 2 y) (5 x + 2 y)

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9 (2 x - 5 y) (2 x - 5 y)

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Solution

The correct option is B $9 (5 x - 2 y) (5 x - 2 y)$
$225 x^{2} - 180 x y + {36 y}^{2}$

$= 9 [{(5 x)}^{2} - 2 (5 x) (2 y) + {(2 y)}^{2}]$

$= 9 {(5 x - 2 y)}^{2}$ .... $[∵ {(a - b)}^{2} = a^{2} - 2 a b + b^{2}]$

$= 9 (5 x - 2 y) (5 x - 2 y)$

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