This document provides instructions to expand binomial expressions up to specific terms. It asks the reader to: 1) Expand (1+x)1/2 up to x3 and then use that to expand (1-x)1/2, stating the interval of validity. 2) Find the first four terms of (1+x)1/3 and then expand (1-x)1/3 to x10, stating the interval of validity.

1. Starter Expand in ascending powers of x up to and including the term in x³. Use your answer to expand and state the interval of validity of your expansion.

2. Objective: to use the binomial expansion to find related expansions

3. Question 1 Expand up to and including the term in x³. Use your answer to expand . State the interval of validity of your expansion.

4. Question 2 Find the first four terms in the expansion of . Hence, expand as far as the term in x 10 . For what values of x is the expansion valid?

5. C4 Textbook Exercise 5 Page 279 Start at Question 10