Given : x^3 512 According to the equation, a^3 b^3=(a b)(a^2+ab+b^2) So we get, x^3 512 #160; =x^3 8^3 Using the equation, =(x 8)(x^2+8x ...

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Factorisation of Quadratic Polynomials- Middle Term Splitting

Factorise : ...

Question

Factorise : $x^{3} - 512$

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Solution

Given : $x^{3} - 512$
According to the equation,
$a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$
So we get,
$x^{3} - 512$ $= x^{3} - 8^{3}$
Using the equation,
$= (x - 8) (x^{2} + 8 x + 8^{2})$
$x^{3} - 512$ $= (x - 8) (x^{2} + 8 x + 64)$

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