1. Ch 2.7 Objective: To combine like terms to simplify expressions.

2. Definition Like Term: Terms that have exactly the same variable (or terms that have no variable) For example: a & a are the same term a & a 2 are NOT the same term

3. Like Terms Unlike Terms 7x -3x 5y -y 10xy 2yx 7x -3y 5y 2a 3ab

4. Sample Problems 1) 5r + r = 6r 2) 5r + 1 + r = 6r + 1 3) 5r + 1 + r 2 = r 2 + 5r + 1 4) -5(2m + 4) – m = -10m – 20 – m = -11m – 20

5. 2 p - 5q 6 1 Simplify by combining like terms. 1) 7x - 4y + 2x - y 2) 3m + 10n - 4m + 1 3) 7x + 3y 4) 6x - (5x) + 2x + (-3) 5) 4k - (2j) - 6k - j 6) 10 - 4x + 3y - 17x 7) 6r - 2.3s - -9r - 3.5s 8) 9) 16 - 14m - - m - 27 10) 8e + 3f + (-5e) - -5f 9x - 5y -m + 10n + 1 7x + 3y 3x - 3 -2k - 3j -21x + 3y + 10 15r - 5.8s -13m - 11 3e + 8f

6. Simplify the following. 1) 10 - 4(x - 5) - 8 2) 6 - 2(5 - x) - (3x + 7) 3) 4x - 5[2(6x - 3) - 7] 4) 5x - 4(7x - 9) - 11 5) 10 + 3(x - 5) - (2x - 9) 6) -4[-(x + 5) - 3(x - 6)] 10 - 4x + 20 - 8 - 4x + 22 6 - 10 + 2x - 3x - 7 - x - 11 4x - 5[12x - 6 - 7] 4x - 5[12x - 13] 4x - 60x + 65 -56x + 65 5x - 28x + 36 - 11 - 23x + 25 10 + 3x - 15 - 2x + 9 x + 4 -4[-x + -5 - 3x + 18] -4[-4x + 13] 16x - 52

7. Simplify by combining like terms. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10)

8. Definition Perimeter The distance around an object. P = 2W + 2L for sides “W” and “L” For example: 12 inches (L) 4 inches (W) (P) = 2W + 2L = 2(4 inches) + 2(12 inches) = 8 inches + 24 inches = 32 inches Reminder: Always look at the UNITS. An exam might give you one side in inches and the other side in feet

9. Irrational Terms Irrational numbers can’t be combined with rational numbers. Like terms Unlike terms