Find the cube of each of the following binomial expressions:$ 2 x+\frac{3}{x} $

Given:

\( 2 x+\frac{3}{x} \)

To do:

We have to find the cube of the given binomial expression.

Solution:

We know that,

$(a+b)^3=a^3 + b^3 + 3a^2b + 3ab^2$

Therefore,

$(2 x+\frac{3}{x})^{3}=(2 x)^{3}+(\frac{3}{x})^{3}+3 \times(2 x)^{2} \times \frac{3}{x}+3 \times 2 x \times (\frac{3}{x})^{2}$

$=8 x^{3}+\frac{27}{x^{3}}+3 \times 4 x^{2} \times \frac{3}{x}+3 \times 2 x \times \frac{9}{x^{2}}$

$=8 x^{3}+\frac{27}{x^{3}}+36 x+\frac{54}{x}$

Hence, $(2 x+\frac{3}{x})^{3}=8 x^{3}+\frac{27}{x^{3}}+36 x+\frac{54}{x}$.

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Updated on: 10-Oct-2022

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