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Day Problems. Evaluate each expression for 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:

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day problems
Day Problems
  • Evaluate each expression for

1. a – 2b 2. b ÷ c

3. a ÷ c 4. -2abc

1 7 the distributive property
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
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
Simplifying an Expression
  • Simplify each expression.

a. 2 (5x + 3)

= 2 (5x) + 2 (3)

= 10x + 6

b.

using the multiplication property of 1
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
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
  • Like terms – have exactly the same variable factors.

Like Terms Not Like Terms

3x and -2x 8x and 7y

-5x2 and 9x2 5y and 2y2

xy and –xy 4y and 5xy

-7x2y3 and 15x2y3 x2y and xy2

  • An algebraic expression in simplest form has NO like terms.
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