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Question
The value of (a + 1)(a – 1)(a2 + 1) is a4 – 1.
Options
True
False
Solution
This statement is True.
Explanation:
Solving it, we get
(a + 1)(a – 1)(a2 + 1) = {(a + 1)(a – 1)} × (a2 + 1)
⇒ (a + 1)(a – 1)(a2 + 1) = (a2 – 1)(a2 + 1) ...[∵ (x + y)(x – y) = x2 – y2; Put x = a and y = 1 ⇒ (a + 1)(a – 1) = a2 – 1]
⇒ (a + 1)(a – 1)(a2 + 1) = a4 – 1 ...[∵ (x2 + y2)(x2 – y2) = x4 – y4; Put x = a and y = 1 ⇒ (a2 + 1)(a2 – 1) = a4 – 1]
Thus, the value of (a + 1)(a – 1)(a2 + 1) is a4 – 1.
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