Transcript Simplify the algebraic expressions.

1-5 Simplifying Algebraic Expressions
Do Now
Evaluate each algebraic expression for y = 3.
1. 3y + y
2. 7y
12
3. 10y – 4y
21
18
4. 5y2 + y - 2
46
1-5 Simplifying Algebraic Expressions
Goal:
Learn to identify like terms and simplify
algebraic expressions.
1-5 Simplifying Algebraic Expressions
In the algebraic expression 5y2 + y - 2, 5y2, y, and
2 are called terms. A term can be a number
(constant), a variable, or a product of numbers and
variables. Terms in an expression are separated by
+ and –.
5y2
term
+
y
term
-
2
term
1-5 Simplifying Algebraic Expressions
In the term 7x, 7 is called the coefficient. A
coefficient is a number that is multiplied by a
variable in an algebraic expression.
Coefficient
Variable
A variable by itself, like y, has a coefficient of 1.
So y = 1y.
1-5 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 are also
like terms.
Like Terms
Unlike
Terms
3x and 2x
w2 and 3w2
5 and 1.8
5x2 and 2x
6a and 6b
3.2 and n
The exponents The variables Only one term
contains a
are different. are different
variable
1-5 Simplifying Algebraic Expressions
Example A
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.
1-5 Simplifying Algebraic Expressions
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
5y3
8z
4y3 and 5y3
5z and 8z
1-5 Simplifying Algebraic Expressions
Combining like terms is like grouping similar objects.
x
x
x
x
4x
+
+
x
x
x
x
5x
x
=
=
x
x
x
x
x
x
x
x
x
9x
To combine like terms that have variables, add or
subtract the coefficients.
1-5 Simplifying Algebraic Expressions
Example B
Simplify the algebraic expressions.
6t – 4t
6t – 4t
6t and 4t are like terms.
2t
Subtract the coefficients.
45x – 37y + 87
In this expression, there are no like terms
to combine.
1-5 Simplifying Algebraic Expressions
Example B
Simplify the algebraic expressions.
3a2 + 5b + 11b2 – 4b + 2a2 – 6
3a2 + 5b + 11b2 – 4b + 2a2 – 6
(3a2 + 2a2) + (5b – 4b) + 11b2 – 6
5a2 + b + 11b2 – 6
Identify like
terms.
Group like
terms.
Add or subtract
the coefficients.
1-5 Simplifying Algebraic Expressions
Example B
Simplify the algebraic expressions.
2(x2 – 13x) + 6
2x 2 – 26x + 6
Distributive Property.
There are no like terms to combine.
1-5 Simplifying Algebraic Expressions
Practice on your own:
Simplify the algebraic expressions.
1-5 Simplifying Algebraic Expressions
Extra Example
Write an expression for the perimeter of the
triangle. Then simplify the expression.
2x + 3
3x + 2
x
Write an expression using
the side lengths.
(x + 3x + 2x) + (2 + 3) Identify and group like
terms.
6x + 5
Add the coefficients.
2x + 3 + 3x + 2 + x
1-5 Simplifying Algebraic Expressions
Extra Example
Write an expression for the perimeter of the
triangle. Then simplify 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
Add the coefficients.
x + 2x + 1 + 2x + 1
1-5 Simplifying Algebraic Expressions
Lesson Quiz
Identify like terms in the list.
5n, 8n
1. 3n2 5n 2n3 8n
2. a5 2a2
a3
3a
4a2
2a2, 4a2
Simplify the algebraic expression.
3. 4a + 3b + 2a
6a + 3b
4. x2 + 2y + 8x2
9x2 + 2y
1-5 Simplifying Algebraic Expressions
Lesson Quiz
5. Write an expression for the perimeter of
the given figure.
2x + 3y
x+y
x+y
2x + 3y
6x + 8y
1-5 Simplifying Algebraic Expressions
Lesson Quiz
6. 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
1-5 Simplifying Algebraic Expressions
Lesson Quiz
7. 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