1. Warm Up Simplify. 1 3 Course 3 4. -5(2x + 6) 3. 6 (x + 2) 2. 16  8x + 4  1. 9 + 13  + 3x

2. Combining Like Terms Distributive Property Tuesday, December 11, 2012

3. Terms in an expression are separated by plus or minus signs. Like terms can be grouped together because they have the same variable raised to the same power. Equivalent expressions have the same value for all values of the variables. Constants such as 4, 0.75, and 11 are like terms because none of them have a variable. Helpful Hint

4. Combine like terms. Identify like terms. Combine coefficients: 14 – 5 = 9 A. 14a – 5a 9a9a B. 7y + 8 – 3y – 1 + y Identify like terms ; the coefficient of y is 1, because 1y = y. 5y + 7 Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7

5. Combine like terms. Identify like terms; the coefficient of q is 1, because 1q = q. Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1c = c. 6 3q3q C. 4q – q D. 5c + 8 – 4c – 2 – c Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6

6. E. 4m + 9n – 2 4m + 9n – 2 Combine like terms. No like terms.

7. When a variable expression has ( ) and we cannot combine what is inside them, we will need to distribute any multiplication attached outside. We will use the distributive property to help. Here’s how: a (b + c) = ab + ac. For example, 2 (x + 4) = 2x + 2(4). Remember to combine any like terms after using the distributive property.

8. To simplify an expression, perform all possible operations, including combining like terms. The Distributive Property states that a(b + c) = ab + ac for all real numbers a, b, and c. For example, 2(3 + 5) = 2(3) + 2(5). Remember!

9. Simplify 6(5 + n) – 2n. Distributive Property. Multiply. 6(5 + n) – 2n 30 + 6n – 2n 6(5) + 6(n) – 2n 30 + 4n Combine coefficients 6 – 2 = 4.

10. Simplify 3(c + 7) – c. Distributive Property. Multiply. 3(c + 7) – c 3c + 21 – c 3(c) + 3(7) – c 2c + 21 Combine coefficients 3 – 1 = 2.

11. 4(3x + 6)  7x 6(x + 5) + 3x Simplify

12. Sometimes using the distributive property will require distributing negative values, or even negative signs resulting from subtractions being changed to additions. Be sure that you continue to change all subtractions to additions 1st, even if this means attaching a negative sign to ( ). 1)2x - 3(x + 4) 1)7y - (y + 4) 3) -8r - 2(r - 5)

13. 1)7(4p - 3) - 7(2p + 3) 1)-2(5x - 3) - 3( x + 2) 1)-5(x + 4) - (3x - 2) 7) - (x + 5) - 2(4x - 7)

14. Homework – WS 2.2 Class activity – with a buddy complete puzzle worksheet