Binomial Theorem

Write the middle term of the following: (x² − 1/x)⁶

Find the term containing x¹⁰ in the expansion of (2x² − 3/x)¹¹.

Find the term independent of x in the expansion of (3x²/2 − 1/3x)⁹.

Using binomial theorem, indicate which number is larger (1.1)¹⁰⁰⁰⁰ or 1000.

In the binomial expansion of (1 + a)^{m + n}, prove that the coefficient of a^m and aⁿ are equal.

Evaluate using binomial theorem: (99)⁵.

The coefficients of (r−1)^th, r^th and (r+1)^th terms in the expansion of (x+1)ⁿ are in the ratio 1 : 3 : 5. Find both n and r.

Find the middle term in the expansion of (3x − x³/6)⁷.

Find the term in the expansion of (x + 1/x)¹² which will be constant.

Expand using binomial theorem: (1 + 2x)⁵.

Expand (1 − x + x²)⁴ using binomial theorem.

Write the general term in the expansion of (a² − b)⁸.

In the expansion of (x − y)¹⁵, calculate the coefficient of x³y¹² and x²y¹³.

Find the 5th term from the end in the expansion of (x³/2 − 2/x²)⁹.

Using Binomial theorem expand:

(i) (x + 1/y)¹¹      (ii) (1 + x + x²)³