Mathematics
Using standard formulae, expand each of the following:
(i) (2 - x)(2 + x)(4 + x2)
(ii) (x + y)(x - y)(x2 + y2)
Expansions
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Answer
We know that,
(a + b)(a - b) = a2 - b2
(i) Given,
⇒ (2 - x)(2 + x)(4 + x2)
⇒ [(2)2 - (x)2](4 + x2)
⇒ (4 - x2)(4 + x2)
⇒ (4)2 - (x2)2
⇒ 16 - x4.
Hence, (2 - x)(2 + x)(4 + x2) = 16 - x4.
(ii) Given,
⇒ (x + y)(x - y)(x2 + y2)
⇒ [(x)2 - (y)2](x2 + y2)
⇒ (x2 - y2)(x2 + y2)
⇒ (x2)2 - (y2)2
⇒ (x4 - y4).
Hence, (x + y)(x - y)(x2 + y2) = (x4 - y4).
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