This document provides examples and explanations of: 1) Using the distributive property to simplify expressions with addition or subtraction inside parentheses, such as 4(a + 9) or 3(a - 8). 2) Combining like terms, where like terms have the same variables raised to the same powers, to simplify algebraic expressions, such as combining -15m + 5 + 20m to -15m + 20m + 5. 3) Homework assignments from the Yellow and Green practice workbooks involving using the distributive property and combining like terms to simplify expressions.

1. 5 Minute Math
1.) (-154) / 11
2.) (-96) / (-3)
3.) 1124 / (-4)
4.) (-78)/ (-2) / (-3)
5.) 430 / (-5) / (-2)
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2. Distributive Property
The product of a and (b + c):
a(b + c) = ab + ac
(b + c)a = ba + ca
The product of a and (b - c)
a(b - c) = ab - ac
(b - c)a = ba - ca
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3. Examples:
1.) 4(x + 2) = 4(x) + 4(2)
4x + 8
2.) (x + 1)9 = 9(x) + 9(1)
9x + 9
3.) 4(x - 2) = 4(x) - 4(2)
4x - 8
4.) (x - 4)6 = (x)6 - (4)6
6x - 24
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4. Rewrite using the distributive property
1.) 4(a + 9) 4.) 3(a - 8)
2.) -6(12 + b) 5.) 9(3 - b)
3.) (c + 1)(5) 6.) (c - 12)(3)
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5. Rewrite using the distributive property
1.) -3(a + 3)
2.) (3 + b)(-6)
3.) -(c - 7)
4.) (5 - d)(-2)
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6. Rewrite using the distributive property
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7. Combining like terms
Like terms: are terms that have the same variable raised to the same power
An expression is simplified if it has no grouping symbols and if all the like
terms have been combined.
Example 1: 11d + 5 d= 16d
Example 2: 17s - 8 - 12s= 5s-8
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8. Try these:
1.) -15m + 5 + 20m
2.) 35y + 20y + 12
3.) 49n - 12a + 8n + 14a
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9. Homework:
8 Yellow Practice workbook 2.6 p. 37-38
8 Green Practice workbook 2.6 & 2.7 p. 41 & 43
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