Find the cube of the following binomial expressions:
$\left( {4 - \dfrac{1}{{3x}}} \right)$
Answer
379.2k+ views
Hint – In this question we simply need to find the cube of the given binomial expression so simply use the direct formula for ${\left( {a - b} \right)^3} = {a^3} - {b^3} - 3{a^2}b + 3a{b^2}$ to get the answer.
Complete step-by-step answer:
Given binomial expression is
$\left( {4 - \dfrac{1}{{3x}}} \right)$
Now we have to find out the cube of this expression.
$ \Rightarrow {\left( {4 - \dfrac{1}{{3x}}} \right)^3}$
Now as we know ${\left( {a - b} \right)^3} = {a^3} - {b^3} - 3{a^2}b + 3a{b^2}$ so, use this property in above equation and expand we have,
$ \Rightarrow {\left( {4 - \dfrac{1}{{3x}}} \right)^3} = {4^3} - {\left( {\dfrac{1}{{3x}}} \right)^3} - 3{\left( 4 \right)^2}\left( {\dfrac{1}{{3x}}} \right) + 3\left( 4 \right){\left( {\dfrac{1}{{3x}}} \right)^2}$
Now simplify the above equation we have,
$ \Rightarrow {\left( {4 - \dfrac{1}{{3x}}} \right)^3} = 64 - \dfrac{1}{{27{x^3}}} - \dfrac{{16}}{x} + \dfrac{4}{{3{x^2}}}$
So, this is the required cube of the given binomial expression.
Note – Whenever we face such types of problems the key concept is to have the basic understanding of the direct algebraic formula for ${\left( {a - b} \right)^3}$. The gist of direct algebraic formula helps in direct simplification of the given problem statement.
Complete step-by-step answer:
Given binomial expression is
$\left( {4 - \dfrac{1}{{3x}}} \right)$
Now we have to find out the cube of this expression.
$ \Rightarrow {\left( {4 - \dfrac{1}{{3x}}} \right)^3}$
Now as we know ${\left( {a - b} \right)^3} = {a^3} - {b^3} - 3{a^2}b + 3a{b^2}$ so, use this property in above equation and expand we have,
$ \Rightarrow {\left( {4 - \dfrac{1}{{3x}}} \right)^3} = {4^3} - {\left( {\dfrac{1}{{3x}}} \right)^3} - 3{\left( 4 \right)^2}\left( {\dfrac{1}{{3x}}} \right) + 3\left( 4 \right){\left( {\dfrac{1}{{3x}}} \right)^2}$
Now simplify the above equation we have,
$ \Rightarrow {\left( {4 - \dfrac{1}{{3x}}} \right)^3} = 64 - \dfrac{1}{{27{x^3}}} - \dfrac{{16}}{x} + \dfrac{4}{{3{x^2}}}$
So, this is the required cube of the given binomial expression.
Note – Whenever we face such types of problems the key concept is to have the basic understanding of the direct algebraic formula for ${\left( {a - b} \right)^3}$. The gist of direct algebraic formula helps in direct simplification of the given problem statement.
Recently Updated Pages
Which of the following would not be a valid reason class 11 biology CBSE

What is meant by monosporic development of female class 11 biology CBSE

Draw labelled diagram of the following i Gram seed class 11 biology CBSE

Explain with the suitable examples the different types class 11 biology CBSE

How is pinnately compound leaf different from palmately class 11 biology CBSE

Match the following Column I Column I A Chlamydomonas class 11 biology CBSE

Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

How many meters are there in a kilometer And how many class 8 maths CBSE

What is pollution? How many types of pollution? Define it

Change the following sentences into negative and interrogative class 10 english CBSE

What were the major teachings of Baba Guru Nanak class 7 social science CBSE

Difference Between Plant Cell and Animal Cell

Give 10 examples for herbs , shrubs , climbers , creepers

Draw a labelled sketch of the human eye class 12 physics CBSE
