Download Combine like terms.

2-9 Combining Like Terms
Bell Work
Evaluate each expression for y = 3.
1. 3y + y
12
2. 7y
21
3. 10y – 4y
18
4. 9y
27
5. y + 5y + 6y
36
6. 10y
30
Course 2
2-9 Combining Like Terms
Learn to combine 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 –.
7x
term
+
5
term
–
3y2 +
term
y+ x
3
term term
In the term 7x, 7 is called
Coefficient
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.
Course 2
Variable
2-9 Combining Like Terms
Term
Coefficient
Course 2
4a
2
3
3k2
x2
x 4.7t
9
4
2
3
3
1
1 4.7
9
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, 1
,
2
and 3.2, are also like terms.
Like Terms
Unlike
Terms
Course 2
w and w
5 and 1.8
7
5x2 and 2x
6a and 6b
3.2 and n
The exponents The variables Only one term
contains a
are different. are different
variable
3x and 2x
2-9 Combining Like Terms
Additional Example 1: Identifying Like Terms
Identify like terms in the list.
3t
5w2
7t
9v
4w2
8v
Look for like variables with like powers.
3t
5w2
7t
9v
Like terms: 3t and 7t
4w2
8v
5w2 and 4w2
9v and 8v
Helpful Hint
Use different shapes or colors to indicate sets of
like terms.
Course 2
2-9 Insert
Lesson
Title
Here
Combining
Like
Terms
Try This: Example 1
Identify like terms in the list.
2x
4y3
8x
5z
5y3
8z
Look for like variables with like powers.
2x
4y3
8x
5z
Like terms: 2x and 8x
Course 2
5y3
8z
4y3 and 5y3
5z and 8z
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.
Course 2
2-9 Combining Like Terms
Additional Example 2C: Combining Like Terms
Combine like terms.
C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6
3a2 + 5b + 11b2 – 4b + 2a2 – 6
(3a2 + 2a2) + (5b – 4b) + 11b2 – 6
5a2 + b + 11b2 – 6
Course 2
Identify like
terms.
Group like
terms.
Add or subtract
the coefficients.
2-9 Insert
Lesson
Title
Here
Combining
Like
Terms
Try This: Example 2A &2B
Combine like terms.
A. 5y + 3y
5y + 3y
8y
5y and 3y are like terms.
Add the coefficients.
B. 23x2 – 13x + 6
In this expression, there are no like terms
to combine.
Course 2
2-9 Insert
Lesson
Title
Here
Combining
Like
Terms
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.
9x2 + 5
Course 2
Add or subtract
the coefficients.
2-9 Insert
Lesson
Title
Here
Combining
Like
Terms
Try This: Example 2D
Combine like terms.
D. 12x2 + y – 3 + x2 - 2y + 1 + 4x
12x2 + y - 3 + x2 - 2y + 1 + 4x
Identify like
terms.
(12x2 + x2 ) + (y – 2y) + (-3 + 1) + 4x Group like
terms.
13x2 - y – 2 + 4x
Add or subtract
or
the coefficients.
2
13x + (- y) + (– 2) + 4x
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
x
3x + 2
Write an expression using
the side lengths.
(x + 3x + 2x) + (2 + 3) Identify and group like
terms.
6x + 5
Combine like terms.
x + 3x + 2 + 2x + 3
Course 2
2-9 Insert
Lesson
Title
Here
Combining
Like
Terms
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 + 2x) + (1 + 1) Identify and group like
terms.
5x + 2
Combine like terms.
x + 2x + 1 + 2x + 1
Course 2
2-9 Combining
Insert Lesson
LikeTitle
Terms
Here
Lesson Quiz: Part 1
Identify like terms.
1. 3n2 5n 2n3 8n
2. a5 2a2
a3
3a
5n, 8n
4a2
2a2, 4a2
Combine like terms.
3. 4a + 3b + 2a
6a + 3b
4. x2 + 2y + 8x2
9x2 + 2y
Course 2
2-9 Combining
Insert Lesson
LikeTitle
Terms
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
Course 2
2-9 Combining
Insert Lesson
LikeTitle
Terms
Here
Lesson Quiz: Part 2
6. Write an expression for the perimeter of
the given figure created using algebra tiles.
8x + 4
Course 2
2-9 Combining
Insert Lesson
LikeTitle
Terms
Here
Lesson Quiz: Part 2
7. Write an expression for the area of the
given figure created using algebra tiles.
x2 + 2x + 2
Course 2
Let’s practice a few more!
http://www.studystack.com/
flashcard-47007