16x^4+54x = 2x(8x^3+27) = 2x[(2x)^3+3^3] = 2x(2x+3)[(2x)^2 2x × 3 + 3^2] = 2x(2x+3)(4x^2 6x+9) ...

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Algebraic Identities

Factorise 16x...

Question

Factorise
$16 x^{4} + 54 x$

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Solution

$16 x^{4} + 54 x = 2 x (8 x^{3} + 27) = 2 x [(2 x)^{3} + 3^{3}] = 2 x (2 x + 3) [(2 x)^{2} - 2 x \times 3 + 3^{2}] = 2 x (2 x + 3) (4 x^{2} - 6 x + 9)$

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