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More Lessons for A Level Maths

Math Worksheets

Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths.

The following diagram shows examples of Binomial Theorem. Scroll down the page for more examples of the Binomial Theorem.

**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 x^{3}

4. Find the binomial expansion of 1/(1 + 4x)^{2} up to and including the term x^{3}

5. Find the binomial expansion of √(1 - 2x) up to and including the term x^{3}. 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 + 11/4x^{2} - 25/8x^{3}.

c) State the range of values of x for which the expansion is valid.

More Lessons for A Level Maths

Math Worksheets

Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths.

The following diagram shows examples of Binomial Theorem. Scroll down the page for more examples of the Binomial Theorem.

Examples:

1. Find the first four terms in the binomial expansion of (1 + 2x)

2. Find the first four terms in the binomial expansion of (2 - x)

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)

4. Find the binomial expansion of 1/(1 + 4x)

5. Find the binomial expansion of √(1 - 2x) up to and including the term x

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)

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 + 11/4x

c) State the range of values of x for which the expansion is valid.

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