1. 2-9 Combining Like Terms Bell Work Evaluate each expression for y = 3.
Course 2
2-9
Combining Like Terms
Bell Work
Evaluate each expression for y = 3.
1. 3y + y
2. 7y
3. 10y – 4y
4. 9y
5. y + 5y + 6y
6. 10y 12 21 18 27 36 30

2. Course 2
2-9
Combining Like Terms
Learn to combine like terms.

3. 7 x 2-9 Combining Like Terms
Course 2
2-9
Combining Like Terms
In the expression 7x + 5, 7x and 5 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 –. x 3
7x – 3y y +
term
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 7 x

4. 2-9 Combining Like Terms Term Coefficient 2 3 x 9 4a 3k2 x2 4.7t 2 3 1
Course 2
2-9
Combining Like Terms
Term
Coefficient 2 3 x 9 4a
3k2 x2
4.7t 2 3 1 9 4 3 1
4.7

5. Course 2
2-9
Combining Like Terms
Like terms are terms with the same variable raised to the same power. The coefficients do not have to be the same. Constants, like 5, , and 3.2, are also like terms. 1 2
Like Terms
Unlike Terms w 7
3x and 2x
w and
5 and 1.8
5x2 and 2x
6a and 6b
3.2 and n
Only one term
contains a
variable
The exponents
are different.
The variables
are different

6. Additional Example 1: Identifying Like Terms
Course 2
2-9
Combining Like Terms
Additional Example 1: Identifying Like Terms
Identify like terms in the list.
3t 5w2 7t 9v w2 8v
Look for like variables with like powers.
3t 5w2 7t 9v w2 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

7. Insert Lesson Title Here
Course 2
2-9
Combining Like Terms
Insert Lesson Title Here
Try This: Example 1
Identify like terms in the list.
2x 4y3 8x 5z y3 8z
Look for like variables with like powers.
2x 4y3 8x 5z y3 8z
Like terms: 2x and 8x 4y3 and 5y3 5z and 8z

8. Additional Example 2A & 2B: Combining Like Terms
Course 2
2-9
Combining Like Terms
Additional Example 2A & 2B: Combining Like Terms
Combine like terms.
A. 6t – 4t
6t – 4t
6t and 4t are like terms. 2t
Subtract the coefficients.
B. 45x – 37y + 87
In this expression, there are no like terms
to combine.

9. Additional Example 2C: Combining Like Terms
Course 2
2-9
Combining Like Terms
Additional Example 2C: Combining Like Terms
Combine like terms.
C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6
Identify like
terms.
3a2 + 5b + 11b2 – 4b + 2a2 – 6
Group like
terms.
(3a2 + 2a2) + (5b – 4b) + 11b2 – 6
5a2 + b + 11b2 – 6
Add or subtract
the coefficients.

10. Insert Lesson Title Here
Course 2
2-9
Combining Like Terms
Insert Lesson Title Here
Try This: Example 2A &2B
Combine like terms.
A. 5y + 3y
5y + 3y
5y and 3y are like terms. 8y
Add the coefficients.
B. 23x2 – 13x + 6
In this expression, there are no like terms
to combine.

11. Insert Lesson Title Here
Course 2
2-9
Combining Like Terms
Insert Lesson Title Here
Try This: Example 2C
Combine like terms.
C. 4x2 + 4y + 3x2 – 4y + 2x2 + 5
4x2 + 4y + 3x2 – 4y + 2x2 + 5
Identify like
terms.
(4x2 + 3x2 + 2x2)+ (4y – 4y) + 5
Group like
terms.
Add or subtract
the coefficients.
9x2 + 5

12. Insert Lesson Title Here
Course 2
2-9
Combining Like Terms
Insert Lesson Title Here
Try This: Example 2D
Combine like terms.
D. 12x2 + y – 3 + x2 - 2y x
12x2 + y x2 - 2y x
Identify like
terms.
(12x2 + x2 ) + (y – 2y) + (-3 + 1) + 4x
Group like
terms.
13x2 - y – 2 + 4x or
13x2 + (- y) + (– 2) + 4x
Add or subtract
the coefficients.

13. Additional Example 3: Geometry Application
Course 2
2-9
Combining Like Terms
Additional Example 3: Geometry Application
Write an expression for the perimeter of the triangle shown. Combine like terms in the expression.
2x + 3
3x + 2 x
Write an expression using
the side lengths.
x + 3x x + 3
(x + 3x + 2x) + (2 + 3)
Identify and group like terms.
6x + 5
Combine like terms.

14. Insert Lesson Title Here
Course 2
2-9
Combining Like Terms
Insert Lesson Title Here
Try This: Example 3
Write an expression for the perimeter of the triangle shown. Combine like terms in the expression.
2x + 1
2x + 1 x
Write an expression using
the side lengths.
x + 2x x + 1
(x + 2x + 2x) + (1 + 1)
Identify and group like terms.
5x + 2
Combine like terms.

15. Insert Lesson Title Here
Course 2
2-9
Combining Like Terms
Insert Lesson Title Here
Lesson Quiz: Part 1
Identify like terms.
1. 3n2 5n 2n3 8n
2. a5 2a2 a3 3a 4a2
Combine like terms.
3. 4a + 3b + 2a
4. x2 + 2y + 8x2
5n, 8n
2a2, 4a2
6a + 3b
9x2 + 2y

16. Insert Lesson Title Here
Course 2
2-9
Combining Like Terms
Insert Lesson Title Here
Lesson Quiz: Part 2
5. Write an expression for the perimeter of the given figure.
2x + 3y
x + y
x + y
2x + 3y
6x + 8y

17. Insert Lesson Title Here
Course 2
2-9
Combining Like Terms
Insert Lesson Title Here
Lesson Quiz: Part 2
6. Write an expression for the perimeter of the given figure created using algebra tiles.
8x + 4

18. Insert Lesson Title Here
Course 2
2-9
Combining Like Terms
Insert Lesson Title Here
Lesson Quiz: Part 2
7. Write an expression for the area of the given figure created using algebra tiles.
x2 + 2x + 2

19. Let’s practice a few more!