Lesson 2: 4-2 Powers of Binomials

1. What do you notice about Pascal's Triangle? Discuss the structure of it.
2. After studying the structure of Pascal's Triangle, try writing it out without looking in your textbook. What strategies help you?
3. Write out the Binomial Theorem. What strategies can you use to help you remember and make sense of this theorem?
4. What does the Binomial Theorem offer that Pascal's triangle does not?

Pascal's triangle

A.APR.5 Know and apply the Binomial Theorem for the expansion of (x+y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.

SAT questions related to polynomial operations: 7-3-2, 6-4-1, 4-3-5, 3-4-6, 1-3-5, 4-4-2, 3-4-33, 8-3-5; dividing polynomials: 7-3-13, 2-3-15

For the expansion of (a+b)^n, the signs of the terms depend on the signs of a and b. The sign of each term is + if both a and b are positive; the sign of each even-numbered term is - if b alone is negative.

A manager plans to hire 8 new employees. Not wanting to appear biased, the manager wants to hire a combination of males and females that has at least a 10% chance of occurring randomly. If there are an equal number of male and female applicants, is the probability of randomly hiring 6 males and 2 females less than 10%?

Students may confuse how to determine the exponents when using Pascal's triangle and the Binomial Theorem.

Have pairs of students work together to make up a jingle or a poem that describes the patterns in the Binomial Theorem.

McGraw Hill resources

McGraw Hill resources