1. 8.3 MULTIPLYING BINOMIALS: Distributive Property: for any real numbers a, b, c, and d: (a+b)(c+d)= ac ac +bd+bd +ad +bc+bc

2. 8.3 MULTIPLYING BINOMIALS: FOIL METHOD: for any real numbers a, b, c, and d in (a+b)(c+d): FIRST: (a)(c) = ac OUTER: (a)(d) = ad INNER: (b)(c) = bc LAST: (b)(d) = bd = ac+ad+bc+bd

3. GOAL:

4. MULTIPLYING BINOMIALS: When multiplying polynomials we must keep in mind the laws of exponents from chapter 7 and the distributive property. Ex: What is the simplest form of: (2x+4)(3x– 7)?

5. FOIL METHOD: FIRST: (2x)(3x) = 6x 2 OUTER: (2x)(-7) = -14x INNER: (4)(3x) = 12x LAST: (4)(-7) = -28 (2x+4)(3x– 7)? 6x 2 -14x+12x-28 6x 2 -2x-28 The simplest form is:6x 2 -2x-28

6. MULTIPLYING BINOMIALS: We can also use a table to: 2x4 3x -7 6x 2 12x -14x-28 6x 2 +12x-14x-28 6x 2 -2x-28

7. REAL-WORLD: What is the area of the frame? 5x-2 7x+1

8. SOLUTION: Using the FOIL method, table or distributive property: 5x-2 7x+1 Area = b.h Area = (7x+1)(5x-2) Area = 35x 2 -14x+5x-2 Total area = 35x 2 -9x-2

9. REAL-WORLD: A factory is looking into making the new label of a can of soup. The can needs to have the dimensions shown in the sketch. what is the total amount of paper needed to make a label?

10. SOLUTION: The label will need to be a rectangle, but the length of the label is the circumference of the can (2πr): x + 4 Area = b.h Area = (2πx+2π)(x+4) Area = 2πx 2 +8xπ+2πx+8π 2πr2πr =2π(x+1) =2πx+2π Total paper needed = 2πx 2 +10xπ+8π

11. VIDEOS: Polynomials Multiplying Multiplying: https://www.khanacademy.org/math/trigonometry/polyn omial_and_rational/polynomial_tutorial/v/multiplying- polynomials

12. CLASSWORK: Page 489-490: Problems: As many as needed to master the concept