Factorize:
$4 a^{2} b - 9 b^{3}$ .

b (2 a + 3 b) (2 a + 3 b)

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b (2 a + 3 b) (a - 3 b)

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b (a + 3 b) (2 a - 3 b)

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b (2 a + 3 b) (2 a - 3 b)

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Solution

The correct option is D $b (2 a + 3 b) (2 a - 3 b)$
$4 a^{2} b - 9 b^{3}$
$= b (4 a^{2} - 9 b^{2})$
$= b ((2 a)^{2} - (3 b)^{2})$
$= b (2 a + 3 b) (2 a - 3 b)$

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