Page 113 - Algebra 1

L E S S O N Combining Like Terms 18
Warm Up
New Concepts
1. Vocabulary A __________ (constant, variable) is a symbol, usually a letter
(2)
Simplify each expression.
2.(0.2)5 3.y3 ·x4 ·y2 ·x5 ·y
(3) (3)
4. Write the phrase “six more than twice a number” as an algebraic expression. (17)
Two or more terms that have the same variable or variables raised to the same power are like terms. Terms with different variables or terms with the same variable or variables raised to a different power are unlike terms.
3x4 + 5y4 + 5x4
Because the variable x has the same power, 3x4 and 5x4 are like terms. Because the variables are not the same, 5y4 and 5x4 are unlike terms. The coefficient is not used to establish whether the terms are like or unlike.
Combining Like Terms Without Exponents
Simplify each expression.
used to represent an unknown number.
Hint
It may be helpful to circle, box, or underline the terms that are alike before combining like terms.
Example
1
a. 5x+7x SOLUTION
5x + 7x
= (5 + 7)x = 12x
b. -4y - (-3y) + 5y SOLUTION
-4y - (-3y) + 5y = (-4 + 3 + 5)y
= 4y
c. 6xy -3a + 4yx SOLUTION
6xy -3a + 4yx
= 6xy + 4yx - 3a = 6xy + 4xy - 3a = 10xy - 3a
Use the Distributive Property. Simplify.
Take the opposite of -3, and then use the Distributive Property.
Simplify.
Rearrange the terms. Rearrange the factors. Add the like terms.
Math Reasoning
Justify Why can the order of the factors in a term be rearranged?
98 Saxon Algebra 1