Martin-Gay, Beginning Algebra, 5ed 11

Gale BachBeginning Algebra

Math 151Fall 2015

Santa Rosa Junior College Mathematics

http://online.santarosa.edu/homepage/gbach/

Martin-Gay, Beginning Algebra, 5ed 22

Why Math?

Martin-Gay, Beginning Algebra, 5ed 33

What is Math?

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Jobs?

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Examples of Algebraic Expressions

5 + 7

6x2 + 7x2

19xy – 30xy + 8

13xy2 – 7x2y + 11xy2

Martin-Gay, Beginning Algebra, 5ed 77

Terms

A term is a number, or the product of a number and variables raised to powers – (the number is called the numerical coefficient).

Examples of Terms

7 (numerical coefficient is 7)

5x3 (numerical coefficient is 5)

4xy2 (numerical coefficient is 4)

z2 = 1 z2 (numerical coefficient is 1)

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Like terms contain the same variables raised to the same powers.

To combine like terms, add or subtract the numerical coefficients (as appropriate), then multiply the result by the common variable factors.

You can combine like terms by adding or subtracting them (this is not true for unlike terms).

Like Terms

Martin-Gay, Beginning Algebra, 5ed 99

5 + 7

6x2 + 7x2

19xy – 30xy + 8

13xy2 – 7x2y +

11xy2

12

13x2

– 11xy + 8

24xy2 – 7x2y

Examples of Combining Terms

Terms Before Combining After Combining Terms

Combining Like Terms

SimplifiedAlgebraicExpressions

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a.) 2(x + y)

= 2x + 2y

Example: Find each product by using the distributive property to remove the parentheses.

Using the Distributive Property

b.) 7(x + 2y – 5z) = 7x + 14y – 35z

c.) – 4(3a – 3b – 10c) = – 12a + 12b + 40c

a.) 2(x + y)

b.) 7(x + 2y – 5z) c.) – 4(3a – 3b – 10c)

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Examples

a.

b.

3 1c. ( 2) (3 2)

4 3x x

d. 3 4 5( 6) 7 (2 1)x x

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Example

Formulas are on page 606 in your textbook.