Ex 8.2 6

Transcript

Ex 8.2, 6 Find the 13th term in the expansion of ﷐﷐9x – ﷐1﷮3﷐﷮x﷯﷯﷯﷮18﷯ , x≠0. We know that General term of expansion (a + b)n is Tr+1 = nCr an–r br We need to calculate 13th term (i.e. T13 = T12+1 ) of expansion ﷐﷐9x – ﷐1﷮3﷐﷮x﷯﷯﷯﷮18﷯ Putting, r = 12 , n = 18 , a = 9x & b = ﷐1﷮3﷐﷮𝑥﷯﷯ T12+1 = 18C12 (9x)18 – 12 × ﷐﷐– ﷐1﷮3﷐﷮x﷯﷯﷯﷮12﷯ = ﷐18!﷮12!(18 − 12)﷯ (9x)6 × ﷐﷐﷐−1﷮3﷯﷯﷮12﷯ ﷐﷐﷐1﷮﷐﷮x﷯﷯﷯﷮12﷯ = ﷐18!﷮12! × 6!﷯ 96 . x6 . (-1)12 . ﷐﷐1﷮3﷯﷯ 12 .﷐﷐﷐1﷮𝑥﷯﷯﷮﷐1﷮2﷯ × 12﷯ = ﷐18 × 17 × 16 × 15 × 14 × 13 × 12!﷮12! ×(6 × 5 × 4 × 3 × 2 ×1 )﷯ . (32)6 . x6 . 1 . ﷐1﷮312﷯ . ﷐1﷮𝑥6﷯ = ﷐18 × 17 × 16 × 15 × 14 × 13 ﷮(6 × 5 × 4 × 3 × 2 )﷯ . 312 . x6 . ﷐1﷮312﷯ . ﷐1﷮𝑥6﷯ = ﷐18 × 17 × 16 × 15 × 14 × 13 ﷮(6 × 5 × 4 × 3 × 2 )﷯ . ﷐312﷮312﷯ . ﷐𝑥6﷮𝑥6﷯ = 18564 × 1 = 18564