Multiplying Binomials

Multiplying Binomials How to use the box method

What is a Binomial? • Binomial: an expression containing two unlike-terms joined by addition or subtraction with at least one variable • Example: • 3x-5 • 2a+4b • 3x2+x

Multiplying Binomials • There are a few different ways to multiply binomials. Most frequently taught and used are: • F-O-I-L • First-Outside -Inside-Last • Not my favorite, too messy • My preference • The Box-Method

Setting up the Box-Method • Let’s Multiply 2 binomials: (x+3)(x+5) • Draw a box with 4 smaller boxes • Spread one binomial across the top • Spread the second binomial down one side, one term per box X +3 X 5 +

Using the Box-Method • Multiply the corresponding terms • Place the products in the box X +3 X2 3X X 5 15 5X +

Pull terms out of the boxes • String them together using addition or subtraction as indicated by the sign of each term. X +3 + + X2 X2 + 3X 3X X 5 15 15 5X 5X +

Pull terms out of the boxes • String them together using addition or subtraction as indicated by the sign of each term. • Combine like-terms X2 + 3X + 5X + 15 X + 3 X2 3X X 5 X2 + 8X+ 15 15 5X +

You Try • (3n+2)(n+3)

You Try • (n-1)(2n-2)

Multiplying Binomials