Q1 of 65 Page 145

Let us factorise the following algebraic expressions:

x(x2 – 1) (x + 2) – 8

As we know that,


a2 – b2 = (a – b)(a + b)


The given expression can be rewritten as:


x(x + 1)(x – 1)(x + 2) – 8


⇒ (x2 + x)(x2 + x – 2) – 8


Let x2 + x = p


⇒ p(p – 2) – 8


⇒ p2 – 2p – 8


⇒ p2 – 4p + 2p – 8


⇒ p(p – 4) + 2(p – 4)


⇒ (p + 2)(p – 4)


On substituting the value of p, we get,


⇒ (x2 + x + 2)(x2 + x – 4)


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