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Question
Simplify the following product:
(x2 + x − 2)(x2 − x + 2)
Solution
Given,
(x2 + x − 2)(x2 − x + 2)
= [x2 + (x − 2)][x2 − (x − 2)]
using identity (a − b)(a + b) = a2 − b2
= (x2)2 − (x − 2)2
using identity, (a − b)2 = a2 − 2ab + b2
= x4 − (x2 − 4x + 4)
= x4 − x2 + 4x − 4
Hence, (x2 + x − 2)(x2 − x + 2) = x4 − x2 + 4x − 4.
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