Question

expand (1/x + y/3)³​

Answer 1

(1/x+y/3)^3

=(1/x)^3+(y/3)^3+3(1/x)^2(y/3)+3(1/x)(y/3)^2

=1/x^3+y^3/27+3y/3x^2+3y^2/9x

Answer 2

Step-by-step explanation:

Solution:-

Given expression

$\rm \bigg( \frac{1}{x} + \frac{y}{3} \bigg) ^{3}$

• ∵ (a + b)³ = a³ + b³ + 3ab(a + b)

• Where, we have to put in our expression a = 1/x and b = y/3.

$\rm\therefore \: \bigg( \frac{1}{x} + \frac{y}{3} \bigg)^{3}$

$\rm= \bigg( \frac{1}{x} \bigg) ^{3} + \bigg( \frac{y}{3} \bigg) ^{3} + 3 \times \frac{1}{x} \times \frac{y}{3} \bigg( \frac{1}{x} + \frac{y}{3} \bigg)^{3}$

$\rm = \frac{1}{ {x}^{3} } + \frac{ {y}^{2} }{27} + \frac{y}{x} \bigg( \frac{1}{x} + \frac{y}{3} \bigg)$

$\rm= \frac{1}{ {x}^{3} } + \frac{ {y}^{3} }{27} + \frac{y}{ {x}^{2} } + \frac{ {y}^{2} }{3x}$

$\rm= \frac{1}{ {x}^{3} } + \frac{y}{ {x}^{2} } + \frac{ {y}^{2} }{3x} + \frac{ {y}^{3} }{27} \: \bf{Ans.}$

Used formulae:-

(a + b)³ = x³ + y³ + 3xy(x + y).

• I hope it's help you.☺