Sec 3 A-Math Binomial Expansions topical questions

Evaluate (6 2) and simplify 7!/5!.

Expand (1 + x)³.

Write down the first two terms of the expansion of (2 + x)⁶ in ascending powers of x.

Expand and simplify (2x + 1)³.

Find the value of (5 3).

Write down the first three terms of the expansion of (1 + 4x)⁵ in ascending powers of x, simplifying each coefficient.

Expand and simplify (3 − x)⁴.

Find the coefficient of x³ in the expansion of (2 + x)⁵.

In the expansion of (1 + kx)⁴, the coefficient of x³ is 32. Find the value of k.

Find the first four terms of the expansion of (2 − x)⁶ in ascending powers of x.

Find the term independent of x in the expansion of (x² + 1/x)⁶.

1. (a)Write down the general term of the expansion.[2]
2. (b)Find the value of r that gives the term independent of x.[2]
3. (c)State the term independent of x.[1]

In the expansion of (2 + kx)⁵, the coefficient of x³ is twice the coefficient of x². Find the value of k.

Show that (1 + x)⁵ + (1 − x)⁵ = 2 + 20x² + 10x⁴.

Find the coefficient of x⁵ in the expansion of (x + 2)⁸.

The coefficient of x² in the expansion of (1 + ax)⁴ is equal to the coefficient of x in the expansion of (1 + 3ax)³.

1. (a)Show that the coefficient of x² in (1 + ax)⁴ is 6a².[2]
2. (b)Show that the coefficient of x in (1 + 3ax)³ is 9a.[2]
3. (c)Hence find the non-zero value of a.[2]