Question

Factorise:
$2y {}^{3} + y {}^{2} - 2y - 1$
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Answer 1

$2 {y}^{3} + {y}^{2} - 2y - 1$

$\sf = 2 {y}^{3} + 2 {y}^{2} - {y}^{ {2} } - y - y - 1$

$\sf= 2 {y}^{2} (y + 1) -y (y + 1) - (y + 1)$

$\sf = (y + 1)(2 {y}^{2} - y - 1)$

$= (y + 1)(2 {y}^{2} - 2y + y - 1)$

$\sf = (y + 1)(2y(y - 1) + 1(y - 1))$

$\sf = (y + 1)(y - 1)(2y + 1)$