1. Algebra I Chapter 1-5 Distributive Property

2. Warm - Up Do the odd problems on the EVALUATING EQUATION worksheet. COPY THE PROBLEMS ON YOUR PAPER AND SOLVE THEM. PLEASE DO NOT WRITE ON MY COPY.

3. Group Work Formulas for the perimeter of a rectangle are used often by surveyors in designing land plots. One surveyor used Formula A; another used Formula B. Do both formulas give the same number for the perimeter? Formula A: P = 2l + 2w Formula B: P = 2(l + w)

4. Commutative, Associative and Identity Properties Quiz State the property each equation represents. 1. 4 + (3 + 2) = (4 + 3) + 2 2. 5 + 3 = 3 + 5 3. 3(5 1) = (3 5)1 4. 7(3) = 3(7) 5. 6(4 + 3) = 6(3 + 4)

5. Vocabulary Distributive Property – 2(x + y) = 2x + 2y We use the distributive property to clear parentheses

6. Examples Use the Distributive Property to write an equivalent expression. 1. 3(x + 2) 2. (s + t + w)6 3. 4(2s + 5)

7. Try This Use the distributive property to write an equivalent expression. 1. 4(x + y + z) 2. (y + 3)5 3. (8a + 3)2 1. 6(x + 2y + 5)

8. Factoring If you reverse the distributive property, we have a process called factoring. ab + ac = a(b + c) EXAMPLES  3x + 3y  5x + 5y + 5z  7y + 14 + 21z  9x + 27 + 9

9. Try This … Factor 5. 5x + 10 6. 12 + 3x 7. 6x + 12 + 9y 8. 5x + 10y + 5

10. Factor and Check by Multiplying 5x + 10 2x + 4y 4a + 4

11. Collecting Like Terms Vocabulary Terms – in an expression like 6s + 6t + 6w, 6s, 6t, and 6w are terms. Like Terms – Terms such as 5x and 4x, whose variable factors are exactly the same.

12. Examples … Collecting Like Terms 3x + 4x x + x 2x + 3y + 5x + 2y 5x ² + x ²

13. Try This Collect Like Terms 9. 6y + 2y 10. 7x + 3y + 5y + 4x 11. 10p + 8q + 4p + 5q 12. 7x ² + x ²