Question

factorise the following: y3+y2-y-1

Answer 1

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$= > {y}^{3} + {y}^{2} - y - 1 \\ \\ = {y}^{2} (y + 1) - 1(y + 1) \\ \\ = (y + 1)( {y}^{2} - 1) \\ \\ = (y + 1)(y - 1)(y + 1) \\ \\ = (y - 1)(y + 1) ^{2}$
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Answer 2

Answer:  The required factored form of the given expression is $(y+1)(y+1)(y-1).$

Step-by-step explanation:  We are given to factorize the following cubic expression :

$E=y^3+y^2-y-1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We will be using the following formula :

$a^2-b^2=(a+b)(a-b).$

The factorization of the given expression (i) is as follows :

$E\\\\=y^3+y^2-y-1\\\\=y^2(y+1)-1(y+1)\\\\=(y+1)(y^2-1)\\\\=(y+1)(y^2-1^2)\\\\=(y+1)(y+1)(y-1).$

Thus, the required factored form of the given expression is $(y+1)(y+1)(y-1).$