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Question
Factorise : 16p4 – 1
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Solution
16p4 – 1 = 24p4 – 1
= (22)2(p2)2 – 12
= (22p2)2 – 12
Comparing with a2 – b2 (a + b)(a – b) where a = 22p2 and b = 1
∴ (22p2)2 – 12 = (22p2 + 1)(22p2 – 1)
= (4p2 + 1)(4p2 – 1)
∴ 16p4 – 1 = (4p2 + 1)(4p2 – 1)
= (4p2 + 1)(22p2 – 12)
= (4p2 + 1)[(2p)2 – 12]
= (4p2 + 1)(2p + 1)(2p – 1) ...[∵ using a2 – b2 = (a + b)(a – b)]
∴ 16p4 – 1 = (4p2 + 1)(2p + 1)(2p – 1)
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