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1-8 Simplifying Algebraic Expressions
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the Day
Lesson Quizzes
1-8 Simplifying Algebraic Expressions
Warm UpEvaluate each expression for y = 3.
1. 3y + y
2. 7y
3. 10y – 4y
4. 9y
5. y + 5y + 6y
12
21
18
27
36
1-8 Simplifying Algebraic Expressions
Problem of the Day
Emilia saved nickels, dimes, and quarters in a jar. She had as many quarters as dimes, but twice as many nickels as dimes. If the jar had 844 coins, how much money had she saved?$94.95
1-8 Simplifying Algebraic Expressions
Learn to simplify algebraic expressions.
1-8 Simplifying Algebraic Expressions
Vocabulary
termcoefficient
1-8 Simplifying Algebraic Expressions
In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by + and –.
7x + 5 – 3y2 + y + x3
term term term term
In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. A variable by itself, like y, has a coefficient of 1. So y = 1y.
Coefficient Variable
term
1-8 Simplifying Algebraic Expressions
Like terms are terms with the same variables raised to the same exponents. The coefficients do not have to be the same. Constants, like 5, , and 3.2, are also like terms.
12
Like Terms
Unlike Terms
3x and 2x
5x2 and 2xThe exponentsare different.
3.2 and nOnly one term
contains avariable
6a and 6bThe variablesare different
w and w7 5 and 1.8
1-8 Simplifying Algebraic Expressions
Identify like terms in the list.
Additional Example 1: Identifying Like Terms
3t 5w2 7t 9v 4w2 8v
Look for like variables with like powers.
3t 5w2 7t 9v 4w2 8v
Like terms: 3t and 7t 5w2 and 4w2 9v and 8v
Use different shapes or colors to indicate sets of like terms.
Helpful Hint
1-8 Simplifying Algebraic Expressions
Check It Out: Example 1
Identify like terms in the list.
2x 4y3 8x 5z 5y3 8z
Look for like variables with like powers.
Like terms: 2x and 8x 4y3 and 5y3 5z and 8z
2x 4y3 8x 5z 5y3 8z
1-8 Simplifying Algebraic Expressions
x
Combining like terms is like grouping similar objects.
+ =x
x
x
x x
x x x
x x x x
x x x x x
4x + 5x = 9x
To combine like terms that have variables, add orsubtract the coefficients.
1-8 Simplifying Algebraic Expressions
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
Additional Example 2: Simplifying Algebraic Expressions
A. 6t – 4t
6t – 4t
2t
6t and 4t are like terms.
Subtract the coefficients.
B. 45x – 37y + 87
In this expression, there are no like termsto combine.
1-8 Simplifying Algebraic Expressions
Additional Example 2: Simplifying Algebraic Expressions
C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6
3a2 + 5b + 11b2 – 4b + 2a2 – 6
5a2 + b + 11b2 – 6
Identify liketerms.
Add or subtractthe coefficients.
(3a2 + 2a2) + (5b – 4b) + 11b2 – 6 Group liketerms.
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
1-8 Simplifying Algebraic Expressions
Check It Out: Example 2
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
A. 5y + 3y
5y + 3y
8y
5y and 3y are like terms.
Add the coefficients.
B. 2(x2 – 13x) + 6
There are no like terms to combine.
2x – 26x + 62 Distributive Property.
1-8 Simplifying Algebraic Expressions
Check It Out: Example 2
C. 4x2 + 4y + 3x2 – 4y + 2x2 + 5
9x2 + 5
Identify liketerms.
Add or subtractthe coefficients.
4x2 + 4y + 3x2 – 4y + 2x2 + 5
Group liketerms.
(4x2 + 3x2 + 2x2)+ (4y – 4y) + 5
Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
1-8 Simplifying Algebraic Expressions
Write an expression for the perimeter of the triangle. Then simplify the expression.
Additional Example 3: Geometry Application
x
2x + 3 3x + 2
2x + 3 + 3x + 2 + x
(x + 3x + 2x) + (2 + 3)
6x + 5
Write an expression usingthe side lengths.Identify and group like terms.Add the coefficients.
1-8 Simplifying Algebraic Expressions
Check It Out: Example 3
x
2x + 12x + 1
x + 2x + 1 + 2x + 1
5x + 2
Write an expression usingthe side lengths.Identify and group like terms.Add the coefficients.
Write an expression for the perimeter of the triangle. Then simplify the expression.
(x + 2x + 2x) + (1 + 1)
1-8 Simplifying Algebraic Expressions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
1-8 Simplifying Algebraic Expressions
Lesson Quiz: Part I
Identify like terms in the list.
1. 3n2 5n 2n3 8n
2. a5 2a2 a3 3a 4a2
Simplify. Justify your steps using the
Commutative, Associative, and Distributive
Properties when necessary.
3. 4a + 3b + 2a
4. x2 + 2y + 8x2
2a2, 4a2
5n, 8n
6a + 3b
9x2 + 2y
1-8 Simplifying Algebraic Expressions
Lesson Quiz: Part II
5. Write an expression for the perimeter of the given figure.
6x + 8y
2x + 3y
2x + 3y
x + yx + y
1-8 Simplifying Algebraic Expressions
1. Identify the like terms in the list.
6a, 5a2, 2a, 6a3, 7a
A. 6a and 2a
B. 6a, 5a2, and 6a3
C. 6a, 2a, and 7a
D. 5a2 and 6a3
Lesson Quiz for Student Response Systems
1-8 Simplifying Algebraic Expressions
2. Identify the like terms in the list.
16y6, 2y5, 4y2, 10y, 16y2
A. 16y6 and 16y2
B. 4y2 and 16y2
C. 16y6 and 2y2
D. 2y5 and 10y
Lesson Quiz for Student Response Systems
1-8 Simplifying Algebraic Expressions
3. Simplify 5x + 2y + 7x. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
A. 5x + 2y + 7x = 5x + 7x + 2y Associative Property
= (5x + 7x) + 2y Commutative Property
= 12x + 2yAdd the coefficients.
B. 5x + 2y + 7x = 5x + 7x + 2yCommutative Property
= (5x + 7x) + 2y Associative Property
= 12x + 2yAdd the coefficients.
Lesson Quiz for Student Response Systems
1-8 Simplifying Algebraic Expressions
4. Simplify 5x2 + 3x + 8x2. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary.
A. 5x2 + 3x + 8x2 = 5x2 + 8x2 + 3x Commutative Property
= (5x2 + 8x2) + 3x Associative Property
= 13x2 + 3xAdd the coefficients.
B. 5x2 + 3x + 8x2 = 3x + 5x2 + 8x2 Associative Property
= (3x + 5x2) + 8x2 Commutative Property
= 8x + 8x2
Add the coefficients.
Lesson Quiz for Student Response Systems
1-8 Simplifying Algebraic Expressions
5. Identify an expression for the perimeter of the given figure.
A. (4x + 5y)(x + 2y) C. 10x + 14yB. D. 5x + 7y
Lesson Quiz for Student Response Systems
4x + 5yx + 2y
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