Question

4
Expand the binomial (x/3 + 2/y)^4​

Answer 1

EXPANSION :

$\mapsto \: \: \sf \: {( \frac{x}{3} + \frac{2}{y} ) }^{4}$

$\implies \sf ^{4} C_0 {( \frac{x}{3} )}^{4} + \: ^{4}C_1 ({ \frac{x}{3} )}^{3} ( \frac{2}{y} ) + ^{4} C_2 {( \frac{x}{3} )}^{2} ( \frac{2}{y} ) {}^{2} + {}^{4} C_3 {( \frac{x}{3} )} {( \frac{2}{y} )}^{3} + \: ^{4} C_4 {( \frac{2}{y}) }^{4}$

$\implies \sf {\frac{x}{3} }^{4} + \: { \frac{8x ^{3} }{27y} }+ \frac{8 {x}^{2} }{9 {y}^{2} } + \frac{32 \: x}{3 \: {y}^{2} } \: + \frac{16 }{ {y}^{4} }$

CONCEPT BOOSTER :

Binomial theorem :

$\rightsquigarrow { \boxed{\sf \: {(x + y)}^{n} = {}^{n} C_0 \: {x}^{n} + {}^{n} C_1 {x}^{n - 1} y + {}^{n} C_2 {x}^{n - 2} {y}^{2} + \dots + {}^{n} C_n \: {y}^{n} }}$

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