18.2 Multiplying Polynomials Expressions Students will Multiply Binomials Model with Polynomial Multiplication

Multiply a monomial and a polynomial Remember the distributive property? It’s back…. 3 𝑥 2 (4 𝑥 2 −7𝑥+8) −7𝑥 (6 𝑥 3 +4𝑥−5)

Write two expressions for the area of the rectangle. 3 𝑥 2 7x - 4

Write two expressions for the area of the rectangle. 4

Write a simplified expression for the area. 3 2 5x

2 3 5x Write a binomial for each side of the rectangle. 2x Now multiply each term of the first binomial by each term of the second binomial. Compare your answer to the last slide.

(x – 9)( x + 8) (2x + 1)( x + 5) (3x – 2)( 4x + 5) Multiply the polynomials. (x – 9)( x + 8) (2x + 1)( x + 5) (3x – 2)( 4x + 5)

Multiply the polynomials. (x + 2)( 𝑥 2 + x - 7) (x - 5)( 3𝑥 2 + x - 2)

A rectangular trivet has a ceramic center and a wooden border A rectangular trivet has a ceramic center and a wooden border. The dimensions of the center and border are shown in the diagram. Write a polynomial that represents the total area of the trivet. x 8 in x 6 in What is the total area of the trivet if the width of the border is 2 inches?

Write a polynomial that represents the area of the shaded region. 8x - 7 3x - 1 3x + 2 2x

Time to Practice http://www.regentsprep.org/Regents/math/ALGEBRA/AV3/Papply.htm http://www.slidermath.com/rpoly/Polym4.shtml

Homework Page 861 #1-24, 26, 27