Using binomial theorem, write down the expansions of the following: (i

1.	Using binomial theorem, write down the expansions of the following: (i)(2x+3y)5 (ii)(2x−3y)4 (iii)(x−1x)6 (iv)(1−3x)7 (v)(ax−bx)6 (vi)(√xa−√ax)6 (vii)(3√x−3√a)6 (viii)(1+2x−3x2)5 (ix)(x+1−1x)3 (x)(1−2x+3x2)3
Answer» Using binomial theorem, write down the expansions of the following: $(i) (2 x + 3 y)^{5}$ $(i i) (2 x - 3 y)^{4}$ $(i i i) {(x - \frac{1}{x})}^{6}$ $(i v) (1 - 3 x)^{7}$ $(v) {(a x - \frac{b}{x})}^{6}$ $(v i) {(\sqrt{\frac{x}{a}} - \sqrt{\frac{a}{x}})}^{6}$ $(v i i) (\sqrt[3]{x} - \sqrt[3]{a})^{6}$ $(v i i i) (1 + 2 x - 3 x^{2})^{5}$ $(i x) {(x + 1 - \frac{1}{x})}^{3}$ $(x) (1 - 2 x + 3 x^{2})^{3}$

Using binomial theorem, write down the expansions of the following: (i)(2x+3y)5 (ii)(2x−3y)4 (iii)(x−1x)6 (iv)(1−3x)7 (v)(ax−bx)6 (vi)(√xa−√ax)6 (vii)(3√x−3√a)6 (viii)(1+2x−3x2)5 (ix)(x+1−1x)3 (x)(1−2x+3x2)3

Answer»

Using binomial theorem, write down the expansions of the following: $(i) (2 x + 3 y)^{5}$

$(i i) (2 x - 3 y)^{4}$

$(i i i) {(x - \frac{1}{x})}^{6}$

$(i v) (1 - 3 x)^{7}$

$(v) {(a x - \frac{b}{x})}^{6}$

$(v i) {(\sqrt{\frac{x}{a}} - \sqrt{\frac{a}{x}})}^{6}$

$(v i i) (\sqrt[3]{x} - \sqrt[3]{a})^{6}$

$(v i i i) (1 + 2 x - 3 x^{2})^{5}$

$(i x) {(x + 1 - \frac{1}{x})}^{3}$

$(x) (1 - 2 x + 3 x^{2})^{3}$