1. Ch 1.3 Distributive Property Objective: To use the distributive property to simplify variable expressions.

2. Property Distributive Property The distributive property is used when multiplying an expression with a group of expressions that are added (or subtracted). For example: a(b + c) = a(b) + a(c) a(b - c) = a(b) - a(c) (b + c)a = (b)a + (c)a (b - c)a = (b)a - (c)a

3. T HE D ISTRIBUTIVE P ROPERTY a(b + c) = ab + ac (b + c)a = ba + ca 2( x + 5 ) 2(x) + 2(5)2x + 10 (x + 5) 2 (x)2 + (5)2 2x + 10 ( 1 + 5x )2 (1)2 + (5x)2 2 + 10x y(1 – y) y(1) – y(y) y – y 2 = = == = = == The product of a and (b + c): U SE THE D ISTRIBUTIVE P ROPERTY

4. Comparison Order of OperationsDistributive Property 6(3 + 5) 6(8) 48 6(3) + 6(5) 18 + 30 48 Why distribute when order of operations is faster ? Use Distributive Property when there is a variable Use Order of Operation to “check” your answer

5. Use the distributive property to simplify. 1) 3(x + 7) 2) 2(a - 4) 3) -7(8 - m) 4) -3(4 + a) 3x 2a -56 -12 Examples + 21 - 8 + 7m - 3a

6. Use the distributive property to simplify. 5) (3 - k)5 7) -4(3 - r) 6) - (2m - 3) 8) (6 - 2y)3 15 -12 -2m 18 Examples - 5k 1 + 3m - 6y

7. (y – 5)(–2) = (y)(–2) + (–5)(–2) = –2y + 10 – (7 – 3x) = (–1)(7) + (–1)(–3x) = –7 + 3x = –3 – 3x (–3)(1 + x) = (–3)(1) + (–3)(x) U SE THE D ISTRIBUTIVE P ROPERTY Remember that a factor must multiply EACH term of an expression. Forgetting to distribute the negative sign when multiplying by a negative factor is a common error.

8. Use the distributive property to simplify. 1) 4(y - 7) 2) 3(b + 4) 3) -5(9 - m) 4) 5(4 - a) 5) (7 - k)6 6) a(c + d) 7) - (-3 - r) 8) 4(x - 8) 9) - (2m + 3) 10) (6 - 2y) -3y Classwork

9. Find the difference mentally. Find the products mentally. The mental math is easier if you think of $11.95 as $12.00 – $.05. Write 11.95 as a difference. You are shopping for CDs. You want to buy six CDs for $11.95 each. Use the distributive property to calculate the total cost mentally. 6(11.95) = 6(12 – 0.05) Use the distributive property. = 6(12) – 6(0.05) = 72 – 0.30 = 71.70 The total cost of 6 CDs at $11.95 each is $71.70. M ENTAL M ATH C ALCULATIONS

10. Geometric Model for Area 3 + 7 4 Two ways to find the total area. Width by total length (Order of Operations) Sum of smaller rectangles (Distributive Property) 4(3 + 7)4(3) + 4(7) 4(3)4(7) = 4 (10) = 12 + 28 40 = 40

11. Geometric Model for Distributive Property 4 x 9 Two ways to find the total area. Width by total lengthSum of smaller rectangles 9(4 + x)9(4) + 9(x) =