
Find the coefficient of in the expansion of .
Answer
489.9k+ views
Hint: Start by grouping the variables inside the expression , then try to find out the highest value of r to be used while expanding the expression . Use the same procedure for further expansion in order to get the desired powers of a, b ,c and d . Separate the coefficient along with the sign obtained and solve it in order to find the required value.
Complete step-by-step answer:
Given,
Let us assume x = (a – b) and y = (d – c)
So the given equation would become as below,
Now, That we need to find the coefficients of
We know , sum of powers or superscripts of a, b, c and d is 5.
Which means we need to check for those coefficients only which make the sum of powers of a, b, c, d as 5.
So we will proceed further by using the binomial expansion formula for
where
So, for =
Substituting the values of x and y, we get
Now applying binomial expansion for both the terms again as per the required exponents of a, b , c, d ,we get
Rearranging the terms we get
Now , the coefficients of will be,
So , the coefficient of is .
Note: Such similar questions can be solved by the same approach used as above. Attention must be given while expanding the binomial expression as any wrong input might lead to vague or incorrect answers. Also value can never be negative, but the coefficients can be due to the nature of variable.
Complete step-by-step answer:
Given,
Let us assume x = (a – b) and y = (d – c)
So the given equation would become as below,
Now, That we need to find the coefficients of
We know , sum of powers or superscripts of a, b, c and d is 5.
Which means we need to check for those coefficients only which make the sum of powers of a, b, c, d as 5.
So we will proceed further by using the binomial expansion formula for
So, for
Substituting the values of x and y, we get
Now applying binomial expansion for both the terms again as per the required exponents of a, b , c, d ,we get
Rearranging the terms we get
Now , the coefficients of
So , the coefficient of
Note: Such similar questions can be solved by the same approach used as above. Attention must be given while expanding the binomial expression as any wrong input might lead to vague or incorrect answers. Also
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