Find the coefficient of: (i)x10 in the expansion of (2x2−1x)20 (ii)x

1.	Find the coefficient of: (i)x10 in the expansion of (2x2−1x)20 (ii)x7 in the expansion of (x−1x2)40 (iii)x−15 in the expansion of (3x2−a3x3)10 (iv)x9 in the expansion of (x2−13x)9 (v)xm in the expansion of (x+1x)n (vi)x in the expansion of (1−2x3+3x5)(1+1x)8 (vii)a5b7 in the expansion of (a−2b)12. (viii)x in the expansion of (1−3x+7x2)(1−x)16
Answer» Find the coefficient of: $(i) x^{10}$ in the expansion of ${(2 x^{2} - \frac{1}{x})}^{20}$ $(i i) x^{7}$ in the expansion of ${(x - \frac{1}{x^{2}})}^{40}$ $(i i i) x^{- 15}$ in the expansion of ${(3 x^{2} - \frac{a}{3 x^{3}})}^{10}$ $(i v) x^{9}$ in the expansion of ${(x^{2} - \frac{1}{3 x})}^{9}$ $(v) x^{m}$ in the expansion of ${(x + \frac{1}{x})}^{n}$ (vi)x in the expansion of $(1 - 2 x^{3} + 3 x^{5}) {(1 + \frac{1}{x})}^{8}$ $(v i i) a^{5} b^{7}$ in the expansion of $(a - 2 b)^{12} .$ (viii)x in the expansion of $(1 - 3 x + 7 x^{2}) (1 - x)^{16}$

Find the coefficient of: (i)x10 in the expansion of (2x2−1x)20 (ii)x7 in the expansion of (x−1x2)40 (iii)x−15 in the expansion of (3x2−a3x3)10 (iv)x9 in the expansion of (x2−13x)9 (v)xm in the expansion of (x+1x)n (vi)x in the expansion of (1−2x3+3x5)(1+1x)8 (vii)a5b7 in the expansion of (a−2b)12. (viii)x in the expansion of (1−3x+7x2)(1−x)16

Answer»

Find the coefficient of:

$(i) x^{10}$ in the expansion of ${(2 x^{2} - \frac{1}{x})}^{20}$

$(i i) x^{7}$ in the expansion of ${(x - \frac{1}{x^{2}})}^{40}$

$(i i i) x^{- 15}$ in the expansion of ${(3 x^{2} - \frac{a}{3 x^{3}})}^{10}$

$(i v) x^{9}$ in the expansion of ${(x^{2} - \frac{1}{3 x})}^{9}$

$(v) x^{m}$ in the expansion of ${(x + \frac{1}{x})}^{n}$

(vi)x in the expansion of $(1 - 2 x^{3} + 3 x^{5}) {(1 + \frac{1}{x})}^{8}$

$(v i i) a^{5} b^{7}$ in the expansion of $(a - 2 b)^{12} .$

(viii)x in the expansion of $(1 - 3 x + 7 x^{2}) (1 - x)^{16}$