Tues, 1/31 SWBAT… multiply a monomial by a polynomial Agenda WU (10 min) Multiplying two binomials (15 min) Warm-Up: Simplify: 3ab(5a2 – a – 2) + 2a(b + 1) Solve: 5(9w + 2) = 3(8w – 7) + 17 Solve: 9c(c – 11) + 10(5c – 3) = 3c(c + 5) + c(6c – 3) – 30 HW#2: Multiplying two binomials 15a3b – 3a2b – 4ab + 2a w = -2/3 c = 0

Multiply two binomials using FOIL method To multiply two binomials, find the sum of the products (x + 2)(x + 3) F L F L I O = (x)(x) + (x)(3) + (2)(x) + (3)(2) O I = x2 + 3x + 2x + 6 = x2 + 5x + 6

Multiply two binomials using FOIL method To multiply two binomials, find the sum of the products of: F the First terms O the Outer terms I the Inner terms L the Last terms (x + 3)(x + 2) F L O I

Find each product: = x2 + 2x – 8 2.) (2y – 7)(3y + 5) = 6y2 – 11y – 35 L 1. (x + 4)(x – 2) 2.) (2y – 7)(3y + 5) = 6y2 – 11y – 35 3.) (4a – 5)(2a – 9) = 8a2 – 46a + 45 = (x)(x) + (x)(-2) + (4)(x) + (4)(-2) I O = x2 – 2x + 4x – 8 = x2 + 2x – 8

Observations The expression (x + 4)(x – 2) is read as “the quantity of x plus 4 times the quantity of x minus 2” FOIL is a memory tool, the order in which the terms are multiplied is not important, as long as four products are found. Notice that when the two linear expressions are multiplied, the result is a quadratic (degree 2).

Antonia is carpeting two of the rooms in her house Antonia is carpeting two of the rooms in her house. The dimensions are shown in the figures. What is the total area to be carpeted. x – 2 x x(x + 3) = x2 + 3x (x – 2)(x + 5) = x2 + 3x – 10 (x2 + 3x) + (x2 + 3x – 10) = 2x2 + 6x – 10 x + 5 x + 3

C

C

D

A rectangular prism has dimensions x, x + 2, 2x + 5 A rectangular prism has dimensions x, x + 2, 2x + 5. Find the volume of the prism in terms of x. x(x + 2) = x2 + 2x (x2 + 2x)(2x + 5) = 2x3 + 9x2 + 10x

Write an expression that represents the area of the court. VOLLEYBALL The dimensions of a volleyball court are represented by a width of 6y – 5 feet and a length of 3y + 4 feet. Write an expression that represents the area of the court. The length of a volleyball court is 31 feet. Find the area of the court. (a) A = LW A = (6y – 5)(3y + 4) = = 18y2 + 24y – 15y – 20 = 18y2 + 9y – 20 (b) L = 3y + 4 31 = 3y + 4 3y = 27 y = 9 18y2 + 9y – 20 18(92) + 9(9) – 20 1458 + 81 – 20 1519 ft2

Write an expression to represent the area of the shaded region. (4x2 – 25) – (x2 – 4) = 3x2 – 21