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Question
Evaluate:
(i) (a + b)(a - b)
(ii) (a2 + b2)(a + b)(a - b); using the result of (i).
(iii) (a4 + b4)(a2 + b2)(a + b)(a - b); using the result of (ii).
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Solution
(i) (a + b)(a - b)
= a (a - b) + b(a - b)
= a2 - ab + ab - b2
= a2 - b2
(ii) (a2 + b2)(a + b)(a - b)
= (a2 + b2)(a2 - b2) ...{from(i)}
= a2 (a2 - b2) + b2 (a2 - b2)
= a4 - a2b2 + a2b2 - b4
= a8 - a4b4 + a4b4 - b8
= a4 - b4
(iii) (a4 + b4)(a2 + b2)(a + b)(a - b)
= (a4 + b4) (a4 - b4) ....{from(ii)}
= a4 (a4 + b4) + b4 (a4 + b4)
= a8 - a4b4 + a4b4 - b8
= a8 - b8
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