1. Equivalent Expressions

2. Equivalent Expressions
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).

3. Equivalent Expressions
Factoring Numerical Expressions
Example 1: Factor each expression as a product of its GCF and the sum
of its other factors.
Strategy:
1.) Find the greatest common factor of the two terms.
2.) Rewrite each term as the product of the GCF and another factor.
3.) Apply the distributive property.
Prime
Numbers
4 • • 14
4 (5 + 14)
Original expression
Rewrite each term as the product of the GCF and another factor.
2 • 2 = 4
Multiply the prime numbers. 4 is the GCF of 20 and 56.
Apply the distributive property.

4. Equivalent Expressions
Factoring Algebraic Expressions
Example 2: Factor each expression as a product of its GCF and the sum
of its other factors.
12x + 18
Strategy:
1.) Find the greatest common factor of the two terms.
2.) Rewrite each term as the product of the GCF and its other factor.
3.) Apply the distributive property.
Prime
Numbers
12x + 18
6 • 2x + 6 • 3
6(2x + 3)
Original expression
Rewrite each term as the product of the GCF and another factor.
2 • 3 = 6
Multiply the prime numbers. 6 is the GCF of 12 and 18.
Apply the distributive property.

5. Equivalent Expressions
Factor each expression as a product of its GCF and the sum of its other factors.
1.) ) ) 5x + 10

6. Equivalent Expressions
Writing Equivalent Expressions
Example: Write four equivalent expressions for each given expression.
8 + 24
8 • • 3
8(1 + 3)
8(3 + 1)
23(3 + 1)
Strategy:
1.) Think about the different ways (properties etc.) that the expression can be written so that its value doesn’t change.
2.) Then, apply what comes to mind.
Original expression
Rewrite the expression using the GCF.
Apply the distributive property.
Apply the commutative property.
Apply exponents

7. Equivalent Expressions
Write four equivalent expressions for each given expression.
1.) ) 25m – 5m

8. Equivalent Expressions
State whether the following expressions are equivalent.
1.) 3x + 12 and 3(x + 4) ) and
3.) 4(2x + 3) and 8x ) 20v – 4v and 16v