martin-gay, beginning algebra, 5ed 11 gale bach beginning algebra math 151 fall 2015 santa rosa...
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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?
Martin-Gay, Beginning Algebra, 5ed 44
Jobs?
Martin-Gay, Beginning Algebra, 5ed 55
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)
Martin-Gay, Beginning Algebra, 5ed 88
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
Martin-Gay, Beginning Algebra, 5ed 1010
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)
Martin-Gay, Beginning Algebra, 5ed 1111
Examples
a.
b.
3 1c. ( 2) (3 2)
4 3x x
d. 3 4 5( 6) 7 (2 1)x x
Martin-Gay, Beginning Algebra, 5ed 1212
Example
Formulas are on page 606 in your textbook.