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Definitions:
Terms – Are the parts of an expression that are added or
subtracted together. For example, the terms of 3x + 10 are 3x
and 10.
Coefficient – Is the number that is multiplied by a variable in an
algebraic expression. For example, the coefficient of 3x is 3.
Equivalent Expressions – Are expressions that have the same
value even though they are written differently. For example, the
expressions 15x + 18 is equivalent to 3(5x + 6).
Factoring Numerical Expressions
Example 1: Factor each expression as a product of its GCF and its other
factors.
20 + 56
Prime
Numbers
2
20
2
2• 2=4
56
10
28
5
14
Multiply the prime numbers. 4
is the GCF of 20 and 56.
20 + 56
4 • 5 + 4 • 14
4 (5 + 14)
Original expression
Rewrite each
term as the
product of the
GCF and another
factor.
Apply the
distributive
property.
Factoring Algebraic Expressions
Example 2: Factor each expression as a product of its GCF and its other
factors.
12x + 18
Prime
Numbers
2
12
3
2• 3=6
18
6
9
2
3
Multiply the prime numbers. 6
is the GCF of 12 and 18.
12x + 18
6 • 2x + 6 • 3
6(2x + 3)
Original expression
Rewrite each
term as the
product of the
GCF and another
factor.
Apply the
distributive
property.
Factor each expression as a product of its GCF and its other
factors.
1.) 6 + 18
2.) 24 + 56
3.) 5x + 10
Writing Equivalent Expressions
Example: Write four equivalent expressions for each given expression.
8 + 24
Original expression
8•1+8•3
Rewrite the expression
using the GCF.
8(1 + 3)
Apply the distributive
property.
8(3 + 1)
Apply the commutative
property.
23(3 + 1)
Apply exponents
Write four equivalent expressions for each given expression.
1.) 9 + 15
2.) 25m – 5m
State whether the following expressions are equivalent.
1.) 3x + 12 and 3(x + 4)
2.) 33 + 10 and 9 + 10
3.) 4(2x + 3) and 8x + 3
4.) 20v – 4v and 16v