If 2s=a+b+c find(s+b)3-(s-b)3-3(s+a)(s-b)(a+b)?
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Sol: Given (s-a)3 + (s-b)3 + 3c(s-a)(s-b) ⇒ (s-a) 3 + (s-b) 3 + 3(2s-a-b)(s-a)(s-b)
⇒ (s - a)3 + (s - b)3 + 3(s - a + s - b)(s - a)(s - b)
let x = (s - a), y = (s - b)
(x + y)3 = x3 + y3 + 3 (x + y) xy
⇒ (s - a + s - b)3 ⇒ (2s- a - b)3 = c3 .
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⇒ (s - a)3 + (s - b)3 + 3(s - a + s - b)(s - a)(s - b)
let x = (s - a), y = (s - b)
(x + y)3 = x3 + y3 + 3 (x + y) xy
⇒ (s - a + s - b)3 ⇒ (2s- a - b)3 = c3 .
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