Answer
Verified
475.5k+ 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
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
How do you graph the function fx 4x class 9 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What organs are located on the left side of your body class 11 biology CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell