# Binomial Expansion Approximations and Estimations

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Examples, solutions, videos, activities, and worksheets that are suitable for A Level Maths.
How to answer questions on Binomial Expansion?

Introduction Infinite series expansion (negative & fractions)
Core 4 - Binomial Expansion (1)

Examples of typical questions (approximations & partial fractions)
Core 4 - Binomial Expansion (2)

Binomial Expansion
Edexcel Core Maths C4 June 2010 Q5(b) : ExamSolutions

Revision of A level binomial expansions - questions and answers 1
A rapid review of the definition of a binomial expansion followed with some illustrations of how and why the coefficients are what they are? Demonstrates that the coefficients have a prescribed pattern.

Revision of A level binomial expansions - questions and answers 2
This video gives precise definitions or formulae for the coefficients of a binomial expansion.

Revision of A level binomial expansions - questions and answers 3
This video presents 4 introductory type questions from A level papers and demonstrates a systematic solution methodology for them.
Example:

1. Find the first 3 terms in ascending powers of x of the binomial expansion (3 + 2x)5, giving each term in its simplest form.
2. Find the first 3 terms in ascending powers of x of the binomial expansion (2 + x)6, giving each term in its simplest form.
3. Find the first 3 terms in ascending powers of x of the binomial expansion (3 - 2x)8, giving each term in its simplest form.

Revision of A level binomial expansions - questions and answers 4
This video presents 4 typical questions from A level papers and demonstrates a systematic solution methodology for solving them.
Example:

1. a) write down the first 3 terms in ascending powers of x of (1 + px)12, where p is a non-zero constant.
b) Given that in the expansion, the coefficient of x is (-q) and the coefficient of x2 is 11q, find the values of p and q.
2. a) Find the first 4 terms in ascending powers of x of the binomial expansion (1 + dx)10, where d is a non-zero constant. Give each term in its simplest form.
b) Given that in the expansion, the coefficient of x3 is double that of x2, find the value of d.
3. a) Find the first 4 terms in ascending powers of x of the binomial expansion (1 + kx)6, where k is a non-zero constant.
b) Given that in the expansion, the coefficients of x and x2 are equal, find (i) the value of k and (ii) the coefficient of x3.
4. a) Find the first 4 terms in ascending powers of x of the binomial expansion (1 + px)9, where p is a non-zero constant.
b) The first three terms as 1, 36x, qx2, where q is constant. Find the values of p and q.

Revision of A level binomial expansions - questions and answers 5
After a very brief reminder of key formulae which will be used, this video presents 4 less typical questions from A level papers and demonstrates a systematic solution methodology for them. [Minor typo in part b of Q4, should ask for q/p.]
Example:

1. a) Write down the first 4 terms in the expansion of (1 + x/10)10, giving each term in its simplest form.
b) Use your expansion to estimate the value of (1.005)10, giving your answer to 4 decimal places.
2. a) Find the first 4 terms in the expansion of (1 + x/4)8, giving each term in its simplest form.
b) Use your expansion to estimate the value of (1.025)8, giving your answer to 4 decimal places.
3. In the binomial expansion of (2 - 5x)20, find an expression for the coefficient of x5.
4. b) In the binomial expansion of (1 + x)40, the coefficients of x4 and x5 are p and q respectively. Find the value of q/p.

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