Binomial expansion
Expand negative and fractional powers, then use the terms to approximate functions.
Choose an available lesson and work at your own pace.
- Binomial expansion with negative and fractional powersExpand binomials with negative and fractional indices using exact coefficients. Understand infinite series, signs, substitutions and truncation with a manual graph and worked practice.
- Expanding (a + bx) to a negative or fractional powerFactor the constant before expanding (a + bx) to negative or fractional powers. Exact coefficients, roots, reciprocals, validity and worked practice.
- Validity of binomial expansionsFind the validity interval of a binomial expansion: linear, quadratic and reciprocal substitutions, combined conditions, endpoints and the difference between convergence and accuracy.
- Finding coefficients in binomial expansionsFind unknown constants and coefficients in binomial products and quotients. Track matching powers, cancellations, even-power substitutions and exact worked solutions.
- Approximations using binomial expansionApproximate roots, reciprocals and quotients with binomial expansion. Choose a small input, calculate absolute and percentage errors and justify rounding with worked practice.
- Binomial expansions using partial fractionsUse partial fractions to expand rational functions: distinct and repeated factors, improper fractions, validity, cancellations and numerical approximations with original worked practice.