Q4 of 65 Page 137

Let us factorise the following algebraic expressions:

4x4 + 81

Given, 4x4 + 81


⇒ 4x4 + 34


⇒ (2x2)2 + 92


⇒ (2x2 + 9)2 – 2(2x2)(9)


⇒ (2x2 + 9)2 – 36x2


⇒ (2x2 + 9)2 – (6x)2


[Since, from the identity III we know that, (x2 – y2) = (x – y)(x + y)]


⇒ ((2x2 + 9) – (6x)) ((2x2 + 9) + (6x))


⇒ (2x2 + 9 – 6x)(2x2 + 9 + 6x)


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