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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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