Thurs, 5/17 SWBAT…multiply two binomials using the FOIL method Agenda WU (5 min) Notes on multiplying two binomials (FOIL method) Warm-Up: 1.) Find the difference & arrange in standard form: (y3 – 10y – 3) – (7y3 + 9y2 – 10) 2.) Find the product & arrange in standard form: -7y²(2y³ + 3xy² – 9xyz) 3.) Solve for x: 5x(x² – 6) + 10x = 5(x3 – 3) + 35 1.) -6y3 – 9y2 – 10y – 7 2.) -14y5 – 21xy4 + 63xy3z 3.) x = -1

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

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) + (2)(3) O I = x2 + 3x + 2x + 6 = x2 + 5x + 6

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

Tues, 3/29 SWBAT…multiply two binomials using the FOIL method Agenda WU (15 min) Review HW#8 (10 min) Quiz (10 min) Warm-Up: 1. (x – 4)(x – 2) 2. (x + 4)2 Square of a Sum 3. (x – 6)2 Square of a Difference 4. (x + 5)(x – 5) Product of a Sum and a Difference Answers: 1.) x2 – 6x – 8 2.) (x + 4)2 = (x + 4)(x + 4) = x2 + 8x + 16 3.) (x – 6)2 = (x – 6)(x – 6) = x2 – 12x + 36 4.) (x + 5)(x – 5) = x2 – 25

C

D

C

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