Factorize the equation $4 a^{2} b - 9 b^{3}$

b (2 a) (2 a - b)

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b (a + b) (3 b)

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b (a + 3 b) (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 $b (2 a + 3 b) (2 a - 3 b)$
$4 a^{2} b - 9 b^{3}$
$= b (4 a^{2} - 9 b^{2})$
Using,
$a^{2} - b^{2} = (a + b) (a - b)$
$= b (2 a + 3 b) (2 a - 3 b)$

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∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} a & b & c & d a & a + b & a + b + c & a + b + c + d a & 2 a + b & 3 a + 2 b + c & 4 a + 3 b + 2 c + d a & 3 a + b & 6 a + 3 b + c & 10 a + 6 b + 3 c + d \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} a & a + b & a + b + c 2 a & 3 a + 2 b & 4 a + 3 b + 2 c 3 a & 6 a + 3 b & 10 a + 6 b + 3 a \end{matrix} ∣ ∣ ∣ ∣ = a^{3}

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