1. 4-3 Equivalent Expressions Learn factor numerical and algebraic expressions and write equivalent numerical and algebraic expression.

2. 4-3 Equivalent Expressions Vocabulary term coefficient equivalent expressions

3. 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. You can use the greatest common factor (GCF) and the Distributive Property to factor numerical expressions. In the term 4x, 4 is called the coefficient. A coefficient is the number that is multiplied by a variable in a algebraic expression.

4. 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.

5. 4-3 Equivalent Expressions The greatest common factor (GCF) is the largest common factor of two or more given numbers. Remember!

6. 4-3 Equivalent Expressions Additional Example 1: Factoring Numerical Expressions Factor the sum of terms as a product of the GCF and a sum. 3.3.3+3.13 27+39 3(9+13) The terms are 27 and 39 The GCF of the terms is 3 Rewrite each term as a product with GCF 3.9+3.13 Apply the distributive law

7. 4-3 Equivalent Expressions Check It Out: Example 1 Factor the sum of terms as a product of the GCF and a sum. 3.5+3.3.5 15+45 27+39 15(1+3) The terms are 15 and 45 The GCF of the terms is 15 Rewrite each term as a product with GCF 1.15+3.15 Apply the Distributive property

8. 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 2.2.3.b+2.2.7 4.3b + 4.7 4(3b+7) The terms are 12b and 28 The GCF of the terms is 2.2 Rewrite each term as a product with GCF Apply the Distributive law

9. 4-3 Equivalent Expressions Check It Out: Example 2 Factor the sum of terms as a product of the GCF and a sum. 2.2.2.2.b+2.2.2.2.2 16b+32 16(b+2) The terms are 16b and 32 The GCF of the terms is 2.2.2.2 Rewrite each term as a product with GCF 16.b+16.2 Apply the distributive property

10. 4-3 Equivalent Expressions There are many other ways to write equivalent expressions for each of the expressions in Example 3. Helpful Hint

11. 4-3 Equivalent Expressions Additional Example 3: Writing Equivalent Expressions Write four equivalent expressions for each given expression. A. 9+15 9+15 3(3+5) 3.3+3.5 3(5+3) 3(8) The terms are 9 and 15 Rewrite each term as a product with GCF Apply the Commutative property Apply the Distributive property Add

12. 4-3 Equivalent Expressions Continued: Example 3 B. 25m-5m 25m-5m (5-1)5m 5.5m-1.5m 4.5m 20m The terms are 25m and 1m Rewrite each term as a product with common factor 5m Subtract Apply the Distributive property Multiply

13. 4-3 Equivalent Expressions C. 2(4p+2) 2(4p+2) 8p+4 2.4p+2.2 4+8p 4+2 3 p Apply the Distributive property Apply the Commutative property Multiply Write the coefficient of 8 as 2 3 Continued: Example 3

14. 4-3 Equivalent Expressions Check It Out: Example 3 Write four equivalent expressions for each given expression. 3(9p+3) 27p+9 3.9p+3.3 9+27p 9+3 3 p Apply the Distributive property Apply the Commutative property Multiply Write the coefficient of 27 as 3 3