1. Example 1 The Distributive Property A. Find (y + 8)(y – 4). Vertical Method Multiply by –4. y + 8 (×) y – 4 –4y – 32–4(y + 8) = –4y – 32 Multiply by y. y 2 + 8yy(y + 8) = y 2 + 8y Combine like terms. y 2 + 4y – 32 y + 8 (×) y – 4

2. Example 1 The Distributive Property B. Find (2x + 1)(x + 6). Vertical Method Multiply by 6. 2x + 1 (×) x + 6 12x + 66(2x + 1) = 12x + 6 Multiply by x. 2x 2 + xx(2x + 1) = 2x 2 + x Combine like terms. 2x 2 + 13x + 6 2x + 1 (×) x + 6

3. Concept

4. Example 2 FOIL Method A. Find (z – 6)(z – 12). (z – 6)(z – 12)= z(z) Answer: z 2 – 18z + 72 F O I L (z – 6)(z – 12)= z(z) + z(–12)(z – 6)(z – 12)= z(z) + z(–12) + (–6)z + (–6)(–12)(z – 6)(z – 12)= z(z) + z(–12) + (–6)z = z 2 – 12z – 6z + 72Multiply. = z 2 – 18z + 72Combine like terms. F (z – 6)(z – 12) OIL

5. Example 2 FOIL Method B. Find (5x – 4)(2x + 8). (5x – 4)(2x + 8) Answer: 10x 2 + 32x – 32 = (5x)(2x) + (5x)(8) + (–4)(2x) + (–4)(8) F OIL = 10x 2 + 40x – 8x – 32Multiply. = 10x 2 + 32x – 32Combine like terms.

6. A.A B.B C.C D.D Example 1 A.c 2 – 6c + 8 B.c 2 – 4c – 8 C.c 2 – 2c + 8 D.c 2 – 2c – 8 A. Find (c + 2)(c – 4).

7. A.A B.B C.C D.D Example 1 A.4x 2 – 11x – 3 B.4x 2 + 11x – 3 C.4x 2 + 13x – 3 D.4x 2 + 12x – 3 B. Find (x + 3)(4x – 1).

8. A.A B.B C.C D.D Example 2 A.x 2 + x – 6 B.x 2 – x – 6 C.x 2 + x + 6 D.x 2 + x + 5 A. Find (x + 2)(x – 3).

9. A.A B.B C.C D.D Example 2 A.5x 2 – 8x + 30 B.6x 2 + 28x – 1 C.6x 2 – 8x – 30 D.6x – 30 B. Find (3x + 5)(2x – 6).

10. Example 3 FOIL Method PATIO A patio in the shape of the triangle shown below is being built in Lavali’s backyard. The dimensions given are in feet. The area A of the triangle is one half the height h times the base b. Write an expression for the area of the patio. Understand We need to find an expression for the area of the patio. We know the measurements of the height and base. Plan Use the formula for the area of a triangle. Identify the height and base. h = x – 7 b = 6x + 7

11. Example 3 FOIL Method Original formula Substitution FOIL method Multiply.

12. Example 3 FOIL Method Combine like terms. Answer: The area of the triangle is 3x 2 – 19x – 14 square units. Distributive Property __ 1 2 CheckChoose a value for x. Substitute this value into (x – 7)(6x + 4) and 3x 2 – 19x – 14. If the result is the same for both expressions, then they are equivalent.

13. A.A B.B C.C D.D Example 3 A.7x + 3 units 2 B.12x 2 + 11x + 2 units 2 C.12x 2 + 8x + 2 units 2 D.7x 2 + 11x + 3 units 2 GEOMETRY The area of a rectangle is the measure of the base times the height. Write an expression for the area of the rectangle.

14. Example 4 The Distributive Property A. Find (3a + 4)(a 2 – 12a + 1). (3a + 4)(a 2 – 12a + 1) = 3a(a 2 – 12a + 1) + 4(a 2 – 12a + 1)Distributive Property = 3a 3 – 36a 2 + 3a + 4a 2 – 48a + 4Distributive Property Answer: = 3a 3 – 32a 2 – 45a + 4Combine like terms.

15. Example 4 The Distributive Property (Vertical Method) A. Find (3a + 4)(a 2 – 12a + 1). (a 2 – 12a + 1) x (3a + 4) 4a 2 – 48a + 4 3a 3 – 36a 2 + 3a 3a 3 – 32a 2 – 45a + 4 Answer: = 3a 3 – 32a 2 – 45a + 4.

16. Example 4 The Distributive Property B. Find (2b 2 + 7b + 9)(b 2 + 3b – 1). (2b 2 + 7b + 9)(b 2 + 3b – 1) = (2b 2 )(b 2 + 3b – 1)+ 7b(b 2 + 3b – 1) + 9(b 2 + 3b – 1) Distributive Property = 2b 4 + 6b 3 – 2b 2 + 7b 3 + 21b 2 – 7b + 9b 2 + 27b – 9 Distributive Property = 2b 4 + 13b 3 + 28b 2 + 20b – 9Combine like terms. Answer: 2b 4 + 13b 3 + 28b 2 + 20b – 9

17. Example 4 The Distributive Property (Vertical Method) B. Find (2b 2 + 7b + 9)(b 2 + 3b – 1). (2b 2 + 7b + 9) (b 2 + 3b – 1) – 2b 2 – 7b – 9 6b 3 + 21b 2 + 27b 2b 4 + 7b 3 + 9b 2 2b 4 + 13b 3 + 28b 2 + 20b – 9 Answer: 2b 4 + 13b 3 + 28b 2 + 20b – 9

18. A.A B.B C.C D.D Example 4 A.12z 3 + 9z 2 + 15z B.8z 2 + 6z + 10 C.12z 3 + z 2 + 9z + 10 D.12z 3 + 17z 2 + 21z + 10 A. Find (3z + 2)(4z 2 + 3z + 5).

19. A.A B.B C.C D.D Example 4 A.12x 4 – 9x 3 – 6x 2 B.7x 3 – x – 1 C.12x 4 – x 3 – 8x 2 – 7x – 2 D.–x 2 + 5x + 3 B. Find (3x 2 + 2x + 1)(4x 2 – 3x – 2).