Question:
The number of terms in the expansion of$ [(a + 4b)^3 (a - 4b)^3]^2$ are
The number of terms in the expansion of$ [(a + 4b)^3 (a - 4b)^3]^2$ are
Updated On: Jul 7, 2022
- 6
- 7
- 8
- 32
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
$[(a + 4b)^3\, (a - 4b)^3]^2 = (a^2 - 16 \,b^2)^6$
No. of terms $= 6 + 1 = 7$
Was this answer helpful?
0
0
Top Questions on binomial expansion formula
- Let the coefficients of three consecutive terms \( T_r \), \( T_{r+1} \), and \( T_{r+2} \) in the binomial expansion of \( (a + b)^{12}\) be in a G.P. and let \( p \) be the number of all possible values of \( r \). Let \( q \) be the sum of all rational terms in the binomial expansion of \( \left( 4\sqrt{3} + 3\sqrt{4} \right)^{12} \). Then \( p + q \) is equal to:
- JEE Main - 2025
- Mathematics
- binomial expansion formula
- Let \( \alpha, \beta, \gamma \) and \( \delta \) be the coefficients of \( x^7, x^5, x^3, x \) respectively in the expansion of \( (x + \sqrt{x^3 - 1})^5 + (x - \sqrt{x^3 - 1})^5, \, x > 1 \). If \( \alpha u + \beta v = 18 \), \( \gamma u + \delta v = 20 \), then \( u + v \) equals:
- JEE Main - 2025
- Mathematics
- binomial expansion formula
- For some \( n \neq 10 \), let the coefficients of the 5th, 6th, and 7th terms in the binomial expansion of \( (1 + x)^{n+4} \) be in A.P. Then the largest coefficient in the expansion of \( (1 + x)^{n+4} \) is:
- JEE Main - 2025
- Mathematics
- binomial expansion formula
- In the expansion of $ \left( \frac{1}{x} + x \sin x \right)^{10} $, the coefficient of the 6th term is equal to $ 7^7g $, then the principal value of $ x $ is.
- COMEDK UGET - 2024
- Mathematics
- binomial expansion formula
- The term independent of $ x $ in the expansion of $ \left( x - \frac{3}{x^2} \right)^{18} $
- JKCET - 2024
- Mathematics
- binomial expansion formula
View More Questions
Notes on binomial expansion formula
Concepts Used:
Binomial Expansion Formula
The binomial expansion formula involves binomial coefficients which are of the form
(n/k)(or) nCk and it is calculated using the formula, nCk =n! / [(n - k)! k!]. The binomial expansion formula is also known as the binomial theorem. Here are the binomial expansion formulas.
This binomial expansion formula gives the expansion of (x + y)n where 'n' is a natural number. The expansion of (x + y)n has (n + 1) terms. This formula says:
We have (x + y)n = nC0 xn + nC1 xn-1 . y + nC2 xn-2 . y2 + … + nCn yn
General Term = Tr+1 = nCr xn-r . yr
- General Term in (1 + x)n is nCr xr
- In the binomial expansion of (x + y)n , the rth term from end is (n – r + 2)th .