
Find the term independent of x in .
Answer
527.1k+ views
Hint: First of all by using the formula for general terms of binomial expansion that is, , write the general term of by taking and n=4. Then put the power of x = 0 to find the term independent of x.
Complete step-by-step answer:
Let us consider the expression given in question as
…………… (1)
We know that, by binomial theorem, we can expand as,
We can also write it as,
Therefore, we get general term in expansion of
By taking we get general term of as,
General term of
Let us consider this general term as,
We know that , applying this in above expression, we get,
Or we get
We can also write above expression as,
Now, we know that . By applying this in above expression, we get
Therefore, we get ……………. (2)
Now, to find the term which is independent of x, we must put the power of x = 0.
Therefore we get, 4-2r=0
By taking the terms containing ‘r’ to one side and constant term to other side, we get,
By dividing 2 on both sides, we get,
Now to get the term independent of x, we put r= 2 in equation (2), we get,
We know that , therefore we get.
Therefore, we get the term independent of x in as .
Note: Students must note that when they are asked to find the term independent of variable, they should always put the power of that variable = 0. Also students must take special care while writing each term and cross check if they have written it correctly or not. Students often make mistakes while writing the powers and this must be avoided.
Complete step-by-step answer:
Let us consider the expression given in question as
We know that, by binomial theorem, we can expand
We can also write it as,
Therefore, we get general term in expansion of
By taking
General term of
Let us consider this general term as,
We know that
Or we get
We can also write above expression as,
Now, we know that
Therefore, we get
Now, to find the term which is independent of x, we must put the power of x = 0.
Therefore we get, 4-2r=0
By taking the terms containing ‘r’ to one side and constant term to other side, we get,
By dividing 2 on both sides, we get,
Now to get the term independent of x, we put r= 2 in equation (2), we get,
We know that
Therefore, we get the term independent of x in
Note: Students must note that when they are asked to find the term independent of variable, they should always put the power of that variable = 0. Also students must take special care while writing each term and cross check if they have written it correctly or not. Students often make mistakes while writing the powers and this must be avoided.
Recently Updated Pages
Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Write the following in Roman numerals 25819 class 7 maths CBSE

Trending doubts
A boat goes 24 km upstream and 28 km downstream in class 10 maths CBSE

The British separated Burma Myanmar from India in 1935 class 10 social science CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Why is there a time difference of about 5 hours between class 10 social science CBSE

What are the public facilities provided by the government? Also explain each facility

Difference between mass and weight class 10 physics CBSE
