2-6 Binomial Theorem 1 2 3 Factorials Pascal’s Triangle & Binomial Theorem 3 Practice Problems

Factorials Written as “n!” Used in the Binomial Theorem and Statistics

Simplifying Factorial Expressions Evaluate

Pascal’s Triangle Expanding the Powers of b+g

Coefficients of Pascal’s Triangle

Coefficients of Pascal’s Triangle Observations for Each Row in the form of (a+b)n There are n+1 terms n is the exponent of a in the first term and the exponent of b in the last term In each term, the exponent of a decreases by one and the exponent of b increases by one The sum of the exponents in each term is n The coefficients are symmetric. They increase at the beginning and decrease at the end

Constructing Pascal’s Triangle Each number in the triangle is the sum of the two directly above it.

Sums of the Rows of Pascal’s Triangle

“Magic 11’s” of Pascal’s Triangle

Binomial Theorem If n is a non-negative integer, then So to expand (x+y)4… Does 1 4 6 4 1 look familiar?

Binomial Theorem Example Expand (2x+y)5 Remember Pascal’s Triangle for (a+b)5 Follow the pattern of the exponents Simplify

Practice Problems