How Do I Multiply Two Binomials?

Table of Contents 82: Warm Up; Guided Practice 83: How Do I Multiply Two Binomials?

Warm-Up Period 3 Factor the following: 1. x2 – 3x + 8 2. x2 + x – 42 3. -5x2 + 10x + 25 4. 5x2 + 25x + 20 (x + 7)(x – 6) Prime For the first section of the warm-up, the students need to find the value of “a” (which shows how much the graph changes in it’s width and direction) and to find the vertex. To find the y-intercept, you need to mulitply the value of a (unknown) * r (1) * s (3), which will equal 18. The students will solve for a and get it to be 6. To determine the vertex, the students will add r + s and divide that be two, getting 2. They then plug that into the equation and solve for g(x), getting -6. -5(x2 – 2x – 5) 5(x + 1)(x + 4)

Warm Up Period 2 Factor the following: 1. x2 + 8x – 36 2. x2 – 9x – 36 3. -6x2 – 36x + 24 4. 4x2 + 16x – 8 (x + 3)(x – 12) Prime -6(x2 + 1)(x – 4) 4(x2 + 4x – 2)

Warm-Up Multiply the following without a calculator: 1. 23 • 56 2. 53 • 17 1288 901

How Do I Multiply Binomials? 1/17/2019

Binomial Two terms that are not alike which are added or subtracted FOIL Method A way of multiplying two binomials F O I L First Terms Outside Terms Inside Terms Last Terms

Example 1: Multiply using FOIL (x + 3)(x + 2) (x + 3)(x + 2) F O I L x • x = x2 x • 2 = 2x 5x 3 • x = 3x 3 • 2 = 6 x2 + 5x + 6

Guided Practice 1 Multiply using FOIL: (x + 4)(x – 2) x2 + 2x – 8

Guided Practice 2 Multiply using FOIL: (x – 7)(x – 6) x2 – 13x + 42

Questions What do the letters in FOIL stand for? What do you think would happen if a was not 1? How would that change the way you multiply? How could you use this to check your work?

Example 2: Multiply vertically (x + 3)(x + 2) x + 3 x + 2 _________ 2x + 6 _____________ x2 + 3x x2 + 5x + 6

Guided Practice 3 Multiply vertically: (x + 4)(x – 2) x2 + 2x – 8

Guided Practice 4 Multiply vertically: (x – 7)(x – 6) x2 – 13x + 42

Questions What do you need to line up in order to multiply vertically? What do you think would happen if a was not 1? How would that change the way you multiply? How could you use this to check your work?

Example 3: Multiply with the box method (x + 3)(x + 2) x + 3 x + 2 x2 3x 2x 6 x2 + 3x + 2x + 6 x2 + 5x + 6

Guided Practice 5 Multiply with the box method: (x + 4)(x – 2)

Guided Practice 6 Multiply with the box method: (x – 7)(x – 6)

Questions How do you need to set up this problem in order to multiply? What do you think would happen if a was not 1? How would that change the way you multiply? How could you use this to check your work? Which method do you like best and why?