Question 88 (xi)

Factorise the following expression.

$a^{3} + a^{2} + a + 1$

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Solution

We have, $a^{3} + a^{2} + a + 1$
$= a^{2} (a + 1) + 1 (a + 1) = (a + 1) (a^{2} + 1)$

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Question 92 (xi)

Factorise the following using the identity $a^{2} - b^{2} = (a + b) (a - b) .$

$y^{3} - \frac{y}{9}$

a^{2} + 2 a b + b^{2} = (a + b)^{2}

9 x^{2} + 24 x + 16

a^{2} - 2 a b + b^{2} = (a - b)^{2}

a^{2} y^{3} - 2 a b y^{2} + b^{2} y

y^{2} + 7 y + 12

l x + m y + m x + l y

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