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प्रश्न
Factorise the following using the identity a2 – b2 = (a + b)(a – b).
(x + y)4 – (x – y)4
उत्तर
We have,
(x + y)4 – (x – y)4 = [(x + y2]2 – [(x – y)2]2
= [(x + y)2 + (x – y)2][(x + y)2 – (x – y2)]
= (x2 + y2 + 2xy + x2 + y2 – 2xy)(x + y + x – y)(x + y – x + y)
= (2x2 + 2y2)(2x)(2y)
= 2(x2 + y2)(2x)(2y)
= 8xy(x2 + y2)
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