Find the cube of each of the following binomial expressions:$ 4-\frac{1}{3 x} $

Given:

\( 4-\frac{1}{3 x} \)

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,

$(4-\frac{1}{3 x})^{3}=(4)^{3}-(\frac{1}{3 x})^{3}-3 \times(4)^{2} \times \frac{1}{3 x}+3 \times 4 \times (\frac{1}{3 x})^{2}$

$=64-\frac{1}{27 x^{3}}-3 \times 16 \times \frac{1}{3 x}+3 \times 4 \times \frac{1}{9 x^{2}}$

$=64-\frac{1}{27 x^{3}}-\frac{16}{x}+\frac{4}{3 x^{2}}$

Hence, $(4-\frac{1}{3 x})^{3}=64-\frac{1}{27 x^{3}}-\frac{16}{x}+\frac{4}{3 x^{2}}$.

Tutorialspoint

Updated on: 10-Oct-2022

64 Views

Kickstart Your Career

Get certified by completing the course

Get Started