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Day Problems. Evaluate each expression for 1. a – 2b2. b ÷ c 3. a ÷ c4. -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

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Day Problems

• Evaluate each expression for

1. a – 2b2. b ÷ c

3. a ÷ c4. -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

b.

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 TermsNot Like Terms

3x and -2x8x and 7y

-5x2 and 9x25y and 2y2

xy and –xy4y and 5xy

-7x2y3 and 15x2y3x2y and xy2

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