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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