4-3 Equivalent Expressions
Learn factor numerical and algebraic
expressions and write equivalent
numerical and algebraic expression.
4-3 Equivalent Expressions
Vocabulary
term
coefficient
equivalent expressions
4-3 Equivalent Expressions
The terms of an expression are the parts of the
expression that are added or subtracted. The
terms of the expressions 140+4x are 140 and
4x.
In the term 4x, 4 is called the coefficient. A
coefficient is the number that is multiplied by
a variable in a algebraic expression.
You can use the greatest common factor
(GCF) and the Distributive Property to factor
numerical expressions.
4-3 Equivalent Expressions
Equivalent expressions are expressions that
have the same value for all the values of the
variables. The expressions 15x+18 and
3(5x+6) are equivalent expressions since
15x+18=3(5x+6) for every value of x.
4-3 Equivalent Expressions
Remember!
The greatest common factor (GCF) is the largest
common factor of two or more given numbers.
4-3 Equivalent Expressions
Additional Example 1: Factoring Numerical
Expressions
Factor the sum of terms as a product of the
GCF and a sum.
27+39
27+39
The terms are 27 and 39
3.3.3+3.13
The GCF of the terms is 3
3.9+3.13
Rewrite each term as a product
with GCF
3(9+13)
Apply the distributive law
4-3 Equivalent Expressions
Check It Out: Example 1
Factor the sum of terms as a product of the
GCF and a sum.
15+45
27+39
The terms are 15 and 45
3.5+3.3.5
The GCF of the terms is 15
1.15+3.15
Rewrite each term as a product
with GCF
15(1+3)
Apply the Distributive property
4-3 Equivalent Expressions
Additional Example 2: Factoring Algebraic
Expressions
Factor the sum of terms as a product of the
GCF and a sum.
12b + 28
12b + 28
The terms are 12b and 28
2.2.3.b+2.2.7
The GCF of the terms is 2.2
4.3b + 4.7
Rewrite each term as a product
with GCF
4(3b+7)
Apply the Distributive law
4-3 Equivalent Expressions
Check It Out: Example 2
Factor the sum of terms as a product of the
GCF and a sum.
16b+32
16b+32
The terms are 16b and 32
2.2.2.2.b+2.2.2.2.2
The GCF of the terms is 2.2.2.2
16.b+16.2
Rewrite each term as a product
with GCF
16(b+2)
Apply the distributive property
4-3 Equivalent Expressions
Helpful Hint
There are many other ways to write equivalent
expressions for each of the expressions in
Example 3.
4-3 Equivalent Expressions
Additional Example 3: Writing Equivalent
Expressions
Write four equivalent expressions for each given
expression.
A. 9+15
9+15
The terms are 9 and 15
Rewrite each term as a product
3.3+3.5
with GCF
3(3+5)
Apply the Distributive property
3(5+3)
Apply the Commutative property
3(8)
Add
4-3 Equivalent Expressions
Continued: Example 3
B. 25m-5m
25m-5m
5.5m-1.5m
The terms are 25m and 1m
Rewrite each term as a product
with common factor 5m
(5-1)5m
Apply the Distributive property
4.5m
Subtract
20m
Multiply
4-3 Equivalent Expressions
Continued: Example 3
C. 2(4p+2)
2(4p+2)
2.4p+2.2
Apply the Distributive property
8p+4
Multiply
4+8p
Apply the Commutative property
4+23p
Write the coefficient of 8 as 23
4-3 Equivalent Expressions
Check It Out: Example 3
Write four equivalent expressions for each given
expression.
3(9p+3)
3(9p+3)
3.9p+3.3
Apply the Distributive property
27p+9
Multiply
9+27p
Apply the Commutative property
9+33p
Write the coefficient of 27 as 33