Factorise:
$27 a^{2} - 75 b^{2}$ .

(3 a + 5 b) (3 a - 5 b)

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3 (3 a + 5 b) (3 a + 5 b)

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(3 a + 5 b) (a - b)

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3 (3 a + 5 b) (3 a - 5 b)

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Solution

The correct option is D $3 (3 a + 5 b) (3 a - 5 b)$
$27 a^{2} - 75 b^{2}$
$= 3 (9 a^{2} - 25 b^{2})$
$= 3 [(3 a)^{2} - (5 b)^{2}]$
$= 3 (3 a + 5 b) (3 a - 5 b)$ (Using $a^{2} - b^{2} = (a + b) (a - b)$ )

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9 a (3 a^{2} - 5 b) - 12 a^{2} (3 a - 5 b)

\frac{3 a + 5 b}{3 a - 5 b} = 5

a : b

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