Lesson: Binomial Theorem: Negative and Fractional exponents Mathematics

In this lesson, we will learn how to use the binomial expansion to expand binomials with negative and fractional exponents.

Lesson Plan

Students will be able to

expand binomial expressions of the form , where is negative or a fraction,
expand binomial expressions of the form , where is negative or a fraction and and are constants,
find the range of values for which a binomial expansion is valid,
approximate values using a binomial expansion and find the percentage error of the approximation when compared to the actual value.

Q1:

Write down the binomial expansion of , up to and including the term in , stating the range of values of for which the expansion is valid.

Q2:

In the binomial expansion of , the coefficient of is . Find the value of the constant and the coefficient of .

Q3:

Write down the first four terms of the binomial expansion of , stating the range of values of for which the expansion is valid.