1. Schema: Simplify

2. Combining Like Terms & Distributive Property Needed review from last year

3. Some Things to Remember x 1x +1x +1x 1 1 Just Watch What Happens

4. Terms vs. Factors

5. How many terms?

6. How many factors does the middle term have?

7. Terms vs. Factors

8. How many terms?

10. Like Terms – have same variable with same exponent 6x + 2x = When combining like terms, only use the coefficients. 6x + 2x =8x 4x + 3y – 2x + 4y = Simplify 2x + 7y Simplify Never, NEVER, combine x’s and y’s or constant terms with variable terms. 2x + 7y ≠ 9xy and 3a + 6 ≠ 9a. Key Skills

11. 7x+ 3y+ 5y– 9x– 17y+ 7x = – 9y – 9x = – 2x + 5y+ 3y– 17y – 2x – 9y Just Watch What Happens

12. TRY THESE 1) 3q + 7q = 10q 2) 4x + 8y – 10x + 3y = – 6x + 11y 4x + 8y – 10x + 3y = 3 + 5x = 3 + 5x ≠ 8x 3(5x) = Review Again 15x

13. In algebraic terms, find the perimeter of the following shape. 2x 4x + 3y 3x – 2y To find the perimeter, add the sides together. P = 3x – 2y + 2x + 3x – 2y + 4x + 3y = 12x – y Key Skills What is the perimeter if x = 5 and y = 8? P = 12(5) – 8 = 52

14. Find the perimeter of the following shape when x = 2. 6x – 2y 5x + y To find the perimeter, add the sides together. P = 5x + y + 5x + y + 6x – 2y = 16x TRY THIS 32 Does the value of y matter in this problem? Obviously Not!

15. P total = 4x + 16 + 6x – 4 Schema: Field 2 Field 1 2x + 5 3 4 3x – 6 A farmer has two rectangular fields. P 1 = 3 + 3 + 2x + 5 + 2x + 5 P 2 = 4 + 4 + 3x – 6 + 3x – 6 P 1 = 4x + 16 P total = 10x + 12 How much fence would the farmer need if x = 5? P 2 = 6x – 4 P total = 10(5) + 12P total = 62 He wants to put a fence around both. In algebraic terms, how much fence would he need?

16. Properties of Addition and Multiplication

17. Commutative Property Commutative Property of Addition-- changing the order in which you add does not change the sum. So, More Examples:

18. Commutative Property So, More Examples:

19. Associative Property Associative Property of Addition-- changing the way the numbers are grouped does not change the sum. Add parenthesis to show Associative Property So,

20. Associative Property Add parenthesis to show Associative Property

21. Identity Property Identity Property of Addition-- if you add zero to a number, you get the same number! 0 is called the identity element of addition!!

22. Identity Property 1 is called the identity element of multiplication!!

23. Inverse Property

24. Additive Inverse Property--a number plus its opposite equals 0.

25. Identify the Property Commutative Prop. Of Multiplication Identity Prop. Of Addition Zero Property Associative Prop. Of Addition Identity Prop. Of Multiplication

26. Distributive Property or Order of Operations Distributive Property It works! Why use the distributive property?

27. Simplify using the distributive property. 1) 2) 3) 4) 5) 6)

28. Simplify using the distributive property. 1) 2) 3) 4) 5) 6)

29. Geometric Model for Distributive Property Two ways to find the area of the rectangle. 4 52 As a wholeAs two parts

30. Geometric Model for Distributive Property Two ways to find the area of the rectangle. 4 52 As a wholeAs two parts same

31. Find the area of the rectangle in terms of x, y and z in two different ways. x yz As a wholeAs two parts

32. Find the area of the rectangle in terms of x, y and z in two different ways. x yz As a wholeAs two parts same

33. Use the distributive property to write an equivalent variable expression. Then simplify. 1) 2) 3) 4) 5) 6)