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Algebraic Identities

Factorize 8x3...

Question

Factorize $8 x^{3} - 125 y^{3} + 180 x y + 216$

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Solution

$8 x^{3} - 125 y^{3} + 180 x y + 216 = (2 x)^{3} + (- 5 y)^{3} + (6)^{3} - 3 \times 2 x (- 5 y) \times 6 = (2 x - 5 y + 6) [(2 x)^{2} + (- 5 y)^{2} + (6)^{2} - 2 x \times (- 5 y) - (- 5 y) \times 6 - 6 \times 2 x] = (2 x - 5 y + 6) (4 x^{2} + 25 y^{2} + 36 + 10 x y + 30 y - 12 x)$

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