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Factorisation Using Algebraic Identities

Factorize: 54...

Question

Factorize:

$54 x^{6} y + 2 x^{3} y^{4}$

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Solution

$54 x^{6} y + 2 x^{3} y^{4} = 2 x^{3} y (27 x^{3} + y^{3}) = 2 x^{3} y [(3 x)^{3} + (y)^{3}] = 2 x^{3} y (3 x + y) [(3 x)^{2} - 3 x \times y + y^{2}] = 2 x^{3} y (3 x + y) (9 x^{2} - 3 x y + y^{2})$

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