(x +1)3 nbsp;+ (x nbsp; ndash; 1)3 =x+1+x 1x+12+x 12 x 1x+1=2xx+12+x 12 x2 1=2xx2+1+2x+x2+1 2x x2+1=2xx2+3 nbsp; ...

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Factorise x+1...

Question

Factorise
(x +1)³ + (x– 1)³

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Solution

(x +1)³ + (x– 1)^{3

$= (x + 1 + x - 1) [{(x + 1)}^{2} + {(x - 1)}^{2} - (x - 1) (x + 1)] = (2 x) [{(x + 1)}^{2} + {(x - 1)}^{2} - (x^{2} - 1)] = 2 x (x^{2} + 1 + 2 x + x^{2} + 1 - 2 x - x^{2} + 1) = 2 x (x^{2} + 3)$}

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