2.1 Simplifying Algebraic Expressions A term is a number or the product of a number and variables raised to powers. The numerical coefficient of a term is the numerical factor. The numerical coefficient of 3x is 3. Example 1 Identify the numerical coefficient of each term: a) 9 x b) 3 y − c) x − d) 2 2.7 xy __________________ contain the same variables raised to the same powers. Terms that are not like terms are called unlike terms. Like Terms Unlike Terms 3x, 2x 5x, 5x 2 Example 2 Indicate whether the terms in each list are like or unlike: a) 6 x , 3x − b) 2 xy − , 2 xy − c) 5ab , 1 2 ba − d) 3 2 2 x yz , 3 3 x yz −
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2.1 Simplifying Algebraic Expressions
A term is a number or the product of a number and variables raised to powers. The
numerical coefficient of a term is the numerical factor. The numerical coefficient of 3x
is 3.
Example 1
Identify the numerical coefficient of each term:
a) 9x
b) 3y−
c) x−
d) 22.7x y
__________________ contain the same variables raised to the same powers. Terms
that are not like terms are called unlike terms.
Like Terms Unlike Terms
3x, 2x 5x, 5x2
Example 2
Indicate whether the terms in each list are like or unlike:
a) 6x , 3x−
b) 2xy− , 2x y−
c) 5ab , 1
2ba−
d) 3 22x yz , 3 3x yz−
Eby, MATH 0310 Spring 2017 Page 2
Simplifying the sum or difference of like terms is called__________________________. To combine like terms add or subtract the numerical coefficient and leave the variable part the SAME!
Example 3
Simplify each expression by combining any like terms:
a) 7 2 4x x− +
b) 9 2 1 6 7y y− + − + + −
c) 2 2 2 23 5 2x y xy x y xy+ − +
Sometimes you will first have to simplify using the ______________________ before
you can combine like terms. To use the distributive property multiply each term inside
the parentheses by what is in front of them. Be careful with negatives!
Example 4
Simplify each expression. Use the distributive property to remove any parentheses.
a) ( 5 6 2 )m n p− − + −
b) 1
(6 9)3x−
Eby, MATH 0310 Spring 2017 Page 3
c) 14(2 6) 4x + −
d) 3(2 5) ( 7)x x− − +
And then there will be times that you need to translate from word to algebraic
expressions. In order to do so you might need to know what some words mean:
+ : sum, added, more than, increased by, plus, total of, together
- : subtracted from, less than, difference between, decreased, minus
x : product, times, any ⅜(etc.) of or % of, multiplied by
÷ : divided, quotient, ratio, over, per
Example 5
a) Triple a number, decreased by six.
b) Six times the sum of a number and two, increased by three.
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2.2 The Addition and Multiplication Properties of Equality
Last time we talked about simplifying expressions, this time we will solve linear
equations. Before we do that let’s look at the difference between expressions and
equations!
Expressions Equations
A ___________________________ is any equation that can be written in the form:
ax b c+ =
where a, b, and c are real numbers and 0a ≠ .
In order to solve linear equations we will need to know some properties!
The ______________________________ states that if a, b, and c are numbers and if
a b= , then a c b c+ = + . This is also true for subtraction! So if a b= , then ca c b= .
Example 1
Solve each equation:
a) 6 18y − = b) 18 5x− = +
c) 2 3
3 4a + = −
Eby, MATH 0310 Spring 2017 Page 5
The ______________________________ states that if a, b, and c are numbers and if
a b= , then a c b c• = • . This is also true for division! So if a b= , then ca c b= .
Example 2
Solve each equation:
a) 2 18y = − b) 83
x= −
c) 2
123a =
Very rarely will we use only one property at a time though!
Example 3
a) 8( 2) 4( 3)y y+ = − b) 8 5 6 3 10z z z− + + = − +
c) 1 1 5 1
6 3 6 2x x− − = +
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And again there will be times that you need to translate from word to algebraic