Transcript Day Problems • Evaluate each expression for1a   , b  , andc  31.

Day Problems
• Evaluate each expression for
3
1
2
a   , b  , andc  
4
3
5
1. a – 2b
2. b ÷ c
3. a ÷ c
4. -2abc
1.7 The Distributive Property
• Distributive Property
– For every real number a, b, and c,
a (b + c) = ab + ac
(b + c) a = ba + ca
a (b – c) = ab – ac
(b – c) a = ba – ca
– Examples:
•
•
•
•
5 (20 + 6) = 5 (20) + 5 (6)
(20 + 6) 5 = 20 (5) + 6 (5)
9 ( 30 – 2) = 9 (30) – 9 (2)
(30 – 2) 9 = 30 (9) – 2 (9)
Simplifying a Numerical Expression
• Use the distributive property to simplify 34 (102).
34 (102) = 34 (100 + 2)
= 34 (100) + 34 (2)
= 3400 + 68
= 3468
Simplifying an Expression
• Simplify each expression.
a. 2 (5x + 3)
= 2 (5x) + 2 (3)
= 10x + 6
1
1 1
b.  3b  2     3b    2  
3
 3  3
2
b
3
Using the Multiplication Property of -1
• Simplify –(6m + 4).
-(6m + 4) = -1 (6m + 4)
= -1 (6m) + (-1)(4)
= -6m – 4
Algebraic Expressions 9/22/10
• Term – a number, a variable, or the product of a
number and one or more variables.
• Ex. 6a2 – 5ab + 3b – 12
• Constant – a term that has no variable.
Ex. -12
• Coefficient – a numerical factor of a term.
Ex. 6, -5, and 3
Like Terms
• Like terms – have exactly the same variable
factors.
Like Terms
3x and -2x
-5x2 and 9x2
xy and –xy
-7x2y3 and 15x2y3
Not Like Terms
8x and 7y
5y and 2y2
4y and 5xy
x2y and xy2
• An algebraic expression in simplest form
has NO like terms.