# Finding Terms in a Binomial Expansion

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Core 4 Maths A-Level Edexcel - Binomial Theorem (1)
Examples:
1. Find the first four terms in the binomial expansion of (1 + 2x)5
2. Find the first four terms in the binomial expansion of (2 - x)6
Core 4 Maths A-Level Edexcel - Binomial Theorem (2)
With negative and fractional n
Examples:
1. Find the first four terms in the binomial expansion of 1/(1 + x)
2. Find the first four terms in the binomial expansion of √(1 - 3x)
3. Find the binomial expansion of (1 - x)1/3 up to and including the term x3
4. Find the binomial expansion of 1/(1 + 4x)2 up to and including the term x3
5. Find the binomial expansion of √(1 - 2x) up to and including the term x3. By substituting in x = 0.001, find a suitable decimal approximation to √2

Core 4 Maths A-Level Edexcel - Binomial Theorem (3)
Binomial theorem of form (ax+b) to the power of n, where n is negative or fractional.
Examples:
1. Use the binomial expansion to find the first four terms of √(4 + x)
2. Use the binomial expansion to find the first four terms of 1/(2 + 3x)2
Core 4 Maths A-Level Edexcel - Binomial Theorem (4)
Partial fractions and binomial theorem
Example:
a) Express (4-5x)/(1+x)(2-x) as partial fractions.
b) Hence show that the cubic approximation of (4-5x)/(1+x)(2-x) is 2 - 7x/2 + 11/4x2 - 25/8x3.
c) State the range of values of x for which the expansion is valid.

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