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Factorisation Using Algebraic Identities

Factorise: 2x...

Question

Factorise:

$2 x^{3} + 54 y^{3} - 4 x - 12 y$

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Solution

$2 x^{3} + 54 y^{3} - 4 x - 12 y$

= 2(x³ + 27y³ - 2x - 6y)

= 2{[(x)³+(3y)³] - 2(x + 3y)}

[Using identity (a³ + b³) = (a + b)(a² - ab + b²)]

=2{[(x + 3y)(x² - 3xy + 9y²)] - 2(x + 3y)}

=2(x + 3y)(x² - 3xy + 9y²- 2)

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