Factorize $8 a^{3} - 27 b^{3} - 36 a^{2} b + 54 a b^{2}$

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Solution

$8 a^{3} - 27 b^{3} - 36 a^{2} b + 54 a b^{2} = (2 a)^{3} - (3 b)^{3} - 3 \times (2 a)^{2} \times 3 b + 3 \times 2 a \times (3 b)^{2} = (2 a - 3 b)^{3} = (2 a - 3 b) (2 a - 3 b) (2 a - 3 b)$

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Factorize $8 a^{3} + 27 b^{3} + 36 a^{2} b + 54 a b^{2}$

8 a^{3} + 27 b^{3} + 36 a^{2} b + 54 a b^{2}

(2 a - 3 b)^{3}

= 8 a^{3} - 27 b^{3} - 36 a^{2} b + 54 a b^{2}

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