Q. 1 E4.3( 16 Votes )

# Let us factorise

As we know that,

a2 – b2 = (a – b)(a + b)

The given expression can be rewritten as:

(x + 1)2(x – 1)2 + 8x(x2 + 1) + 19x2

Using (a – b)2 = a2 + b2 – 2ab, and

(a + b)2 = a2 + b2 + 2ab

(x2 + 1 + 2x)(x2 + 1 – 2x) + 8x(x2 + 1) + 19x2

Let x2 + 1 =p

(p + 2x)(p – 2x) + 8xp + 19x2

p2 – 4x2 + 8xp + 19x2

p2 + 8xp + 15x2

p2 + 3xp + 5xp + 15x2

p(p+3x) + 5x(p + 3x)

(p + 5x)(p + 3x)

On substituting the value of p, we get,

(x2 + 5x + 1)(x2 + 3x + 1)

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