# Ex 8.1, 5

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Ex8.1, 5 Expand x+1x6 We know that (a + b)n = nC0 an b0 + nC1 an – 1 b1 + nC2 an – 2 b2 + …. …. + nCn – 1 a1 bn – 1 + nCn a0 bn Hence (a + b)6 = = 6!0! 6 −0! a6 × 1 + 6!1 ! 6 −1 ! a5 b + 6!2!6 −2! a4 b2 + 6!3 !6 −3! a3 b3 + 6!4 ! 6 − 4 !a2 b4 + 6!5 ! 6 −5! ab5 + 6!6 ! 6 −6 ! 1 × b6 = 6!1 × 6! a6 + 6!1 × 5! a5 b + 6!2! × 4! a4 b2 + 6!3 ! 3! a3 b3 + 6!4 ! 2! a2 b4 + 6!5 ! ×1 a b5 + 6!6 ! × 1 b6 = 6!6! a6 + 6 ×5!5! a5b + 6 ×5 ×4!2 × 4! a4 b2 + 6 ×5 ×4 × 3!3 × 2 × 1 × 3! a3 b3 + 6 × 5 × 4!2 × 1 × 4! a2 b4 + 6 × 5!1 × 5! ab5 + 6!6! b6 = a6 + 6a5b + (3 × 5)a4b2 + (5 × 4)a3b3 + (3 × 5)a2b4 + 6ab5 + b6 = a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + b6 Thus, (a + b)6 = a6 + 6a5b + 15a4b2 + 20a3b3 + 15a2b4 + 6ab5 + b6 We need to find 𝑥 +1𝑥6 Putting a = x & b = 1𝑥 𝑥 +1𝑥6 = (x)6 + 6 (x)5 1𝑥 + 15 (x4) 1𝑥2 + 20 (x)3 1𝑥3 + 15 (x)2 1𝑥4 + 6(x)1 1𝑥5 + 1𝑥6 = x6 + 6x4 + 15x2 + 20 + 15 × 1𝑥2 + 6 1𝑥4 + 1𝑥6 = x6 + 6x4 + 15x2 + 20 + 15𝑥2 + 6𝑥4 + 1𝑥6

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