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3-2 Simplifying Algebraic Expressions
Simplifying
Expressions
Evaluating Algebraic
Expressions
Essential Question
How are expressions simplified
by combining like terms?
How does the distributive
property help to simplify
expressions?
3-2 Simplifying Algebraic Expressions
Evaluating
Algebraic Expressions
Vocabulary
term
like term
coefficient
constant
equivalent expression
3-2 Simplifying Algebraic Expressions
In the expression below, 7x, 5, 3y, and 2x are
Evaluating
Expressions
terms.
A term canAlgebraic
be a number, a
variable, or
a product of numbers and variables. Terms in
an expression are separated by plus or minus
signs.
Constant
Coefficients
3-2 Simplifying Algebraic Expressions
Like terms, such as 7x and 2x, can be grouped
together
because they
have the same
variable
Evaluating
Algebraic
Expressions
raised to the same power. Often, like terms have
different coefficients. A coefficient is a number
that is multiplied by a variable in an algebraic
expression. A constant is a number that does
not change. Constants, such as 4, 0.75, and 11,
are also like terms.
When you combine like terms, you change the
way an expression looks but not the value of the
expression. Equivalent expressions have the
same value for all values of the variables.
3-2 Simplifying Algebraic Expressions
Additional Example 1: Combining Like Terms in
One-Variable Expressions
Evaluating Algebraic Expressions
Combine like terms.
A. 14a – 5a
9a
Identify like terms.
B. 7y + 8 – 3y – 1 + y
Identify like terms; the
coefficient of y is 1, because
1y = y.
5y + 7
Combine coefficients: 14 – 5 = 9
Combine coefficients: 7 – 3 + 1 = 5
and 8 – 1 = 7
3-2 Simplifying Algebraic Expressions
Evaluating Algebraic Expressions
Helpful Hint
When you rearrange terms, move the
operation in front of each term with that
term.
3-2 Simplifying Algebraic Expressions
Additional Example 2A: Combining Like Terms in
Two-Variables Expressions
Evaluating Algebraic Expressions
Combine like terms.
9x + 3y – 2x + 5
9x + 3y – 2x + 5
Identify like terms.
7x + 3y + 5
Combine coefficients: 9 – 2 = 7
3-2 Simplifying Algebraic Expressions
Additional Example 2B: Combining Like Terms in
Two-Variable Expressions
Evaluating Algebraic Expressions
Combine like terms.
5t + 7p – 3p – 2t
5t + 7p – 3p – 2t
Identify like terms.
3t + 4p
Combine coefficients: 5 – 2 = 3
and 7 – 3 = 4
3-2 Simplifying Algebraic Expressions
Additional Example 2C: Combining Like Terms in
Two-Variable Expressions
Evaluating Algebraic Expressions
Combine like terms.
4m + 9n – 2
4m + 9n – 2
No like terms.
3-2 Simplifying Algebraic Expressions
Check It Out! Example 2
Combine like terms.
Evaluating Algebraic Expressions
A. 2x + 5x – 4y + 3
2x + 5x – 4y + 3
Identify like terms.
7x – 4y + 3
Combine coefficients: 2 + 5 = 7
B. 9d + 7c – 4d – 2c
9d + 7c – 4d – 2c
Identify like terms.
5d + 5c
Combine coefficients: 9 – 4 = 5
and 7 – 2 = 5
C. 8g + c – 6
8g + c – 6
No like terms.
3-2 Simplifying Algebraic Expressions
Evaluating Algebraic Expressions
To simplify an expression, perform all
possible operations, including
combining like terms. You may need to
use the Associative, Commutative, or
Distributive Properties.
3-2 Simplifying Algebraic Expressions
THE DISTRIBUTIVE PROPERTY
The
product of a and (bAlgebraic
+ c):
Evaluating
Expressions
a(b + c) = ab + ac
2(x + 5) = 2(x) + 2(5) = 2x + 10
(b + c)a = ba + ca
(x + 5)2 = (x)2 + (5)2 = 2x + 10
y(1 – y) = y(1) – y(y) = y – y 2
(1 + 5x)2 = (1)2 + (5x)2 = 2 + 10x
3-2 Simplifying Algebraic Expressions
Remember that a factor must multiply each term of an expression.
Evaluating Algebraic Expressions
Distribute the –3.
(–3)(1 + x) = (–3)(1) + (–3)(x)
= –3 – 3x
Simplify.
(y – 5)(–2) = (y)(–2) + (–5)(–2)
Distribute the –2.
= –2y + 10
–(7 – 3x) = (–1)(7) + (–1)(–3x)
= –7 + 3x
Simplify.
–a = –1 • a
Simplify.
Forgetting to distribute the negative sign when multiplying by a
negative factor is a common error.
3-2 Simplifying Algebraic Expressions
Additional Example 3: Using the Distributive
Property to Simplify
Evaluating Algebraic Expressions
Simplify 6(5 + n) – 2n.
6(5 + n) – 2n
6(5) + 6(n) – 2n
Distributive Property
30 + 6n – 2n
Multiply.
30 + 6n – 2n
Identify like terms.
30 + 4n
Combine coefficients: 6 – 2 = 4.
3-2 Simplifying Algebraic Expressions
Check It Out! Example 3
Evaluating
Simplify
3(c + 7) Algebraic
– c.
Expressions
3(c + 7) – c
3(c) + 3(7) – c
Distributive Property
3c + 21 – c
Multiply.
3c + 21 – c
Identify like terms.
2c + 21
Combine coefficients: 3 – 1 = 2.