The “coefficients only” column matches the numbers in Pascal's Triangle. Pascal's Triangle, named for the French mathematician Blaise Pascal (1623–1662), is a triangular array of numbers in which the first and last number of each row is 1. Each of the other numbers in the row is the sum of the two numbers above it.
For example, to generate row 5, use the sums of the adjacent elements in the row above it.
Problem 1 Using Pascal's Triangle
What is the expansion of
Plan
What row of Pascal's Triangle should you use for this expansion?
The expression is raised to the 6th power so use the 6th row.
✓ Got It?
- What is the expansion of
The Binomial Theorem gives a general formula for expanding a binomial.
Take Note Theorem: Binomial Theorem
For every positive integer n,
where
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions