Transcript Beginning & Intermediate Algebra. 4ed

Chapter 2
Equations,
Inequalities, and
Problem Solving
§ 2.1
Simplifying Algebraic
Expressions
Terms
A term is a number, or the product of a number and
variables raised to powers – (the number is called a
coefficient).
Examples of Terms
7
(coefficient is 7)
5x3
(coefficient is 5)
4xy2
(coefficient is 4)
z2
(coefficient is 1)
Martin-Gay, Beginning and Intermediate Algebra, 4ed
3
Like Terms
Like terms contain the same variables raised to the
same powers.
You can combine like terms by adding or
subtracting them (this is not true for unlike terms).
To combine like terms, add or subtract the
numerical coefficients (as appropriate), then
multiply the result by the common variable factors.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
4
Combining Like Terms
Examples of Combining Terms
Terms Before Combining
After Combining Terms
6x2 + 7x2
13x2
19xy – 30xy
– 11xy
13xy2 – 7x2y
Can’t be combined
(since the terms are not
like terms)
Martin-Gay, Beginning and Intermediate Algebra, 4ed
5
Using the Distributive Property
Example: Find each product by using the distributive
property to remove the parentheses.
a.) 2(x + y)
b.) 7(x + 2y – 5z)
c.) – 4(3a – 3b – 10c)
a.) 2(x + y) = 2x + 2y
b.) 7(x + 2y – 5z) = 7x + 14y – 35z
c.) – 4(3a – 3b – 10c) = – 12a + 12b + 40c
Martin-Gay, Beginning and Intermediate Algebra, 4ed
6
Word Phrases as Algebraic Expressions
Addition
(+)
sum
plus
added to
more than
increased by
total
Subtraction
(–)
difference
minus
subtract
less than
decreased by
less
Multiplication
(·)
product
times
multiply
multiplied by
of
double/triple
Martin-Gay, Beginning and Intermediate Algebra, 4ed
Division
()
quotient
divide
shared equally
among
divided by
divided into
7
Word Phrases as Algebraic Expressions
Example:
Write as an algebraic expression. Use x to represent “a number.”
a.) 5 decreased by a number
b.) The quotient of a number and 12
a.) In words: 5
decreased by
a number
–
Translate: 5
x
The quotient of
b.) In words: a number
Translate:
x
and
12

12
or
x
12
Martin-Gay, Beginning and Intermediate Algebra, 4ed
8