4 3 Equivalent Expressions I CAN factor numerical

4 -3 Equivalent Expressions I CAN factor numerical expressions. I CAN factor algebraic expressions. I CAN write equivalent numerical and algebraic expressions.

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 expression 140+4 x are 140 and 4 x. In the term 4 x, 4 is called the coefficient. A coefficient is the number that is multiplied by a variable in an algebraic expression. You can use the greatest common factor (GCF) and the Distributive Property to factor numerical expressions.

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 Example 1: Factoring Numerical Expressions A. Factor the sum of terms as a product of the GCF and a sum. 27+39 The terms are 27 and 39 The GCF of the terms is 3 Rewrite each term as a product with GCF 3(9+13) Apply the distributive property

4 -3 Equivalent Expressions Example 1: Factoring Numerical Expressions B. Factor the sum of terms as a product of the GCF and a sum. 35+15 The terms are 35 and 15 The GCF of the terms is 5 5∙ 7+5∙ 3 Rewrite each term as a product with GCF 5(7+3) Apply the distributive property

4 -3 Equivalent Expressions You Try! Example 1 Factor the sum of terms as a product of the GCF and a sum. A. 14+42 B. 20+56 14∙ 1+14∙ 3 4∙ 5+4∙ 14 14(1+3) 4(5+14)

4 -3 Equivalent Expressions Example 2: Factoring Algebraic Expressions A. Factor the sum of terms as a product of the GCF and a sum. 12 b + 28 The terms are 12 b and 28 The GCF of the terms is 4 4∙ 3 b + 4∙ 7 Rewrite each term as a product with GCF 4(3 b+7) Apply the distributive property

4 -3 Equivalent Expressions Example 2: Factoring Algebraic Expressions B. Factor the sum of terms as a product of the GCF and a sum. 16 b+32 The terms are 16 b and 32 The GCF of the terms is 16 16∙b+16∙ 2 Rewrite each term as a product with GCF 16(b+2) Apply the distributive property

4 -3 Equivalent Expressions You Try! Example 1 Factor the sum of terms as a product of the GCF and a sum. A. 12 b+28 B. 40 y 30 y 4∙ 3 b+4∙ 7 10 y∙ 4 10 y∙ 3 4(3 b+7) 10 y(4 3)

4 -3 Equivalent Expressions Reflection CAN YOU factor numerical and algebraic expressions?

4 -3 Equivalent Expressions Lesson Quiz Factor the sum of terms as a product of the and a sum 1. 45 + 15 15(3+1) 2. 24 + 40 8(3+5) 3. 16 y + 36 4(4 y+9) 4. 90 + 60 s 30(3+2 s) GCF

4 -3 Equivalent Expressions HOMEWORK

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 Equivalent expressions are expressions that have the same value for all the values of the variables. The expressions 15 x+18 and 3(5 x+6) are equivalent expressions since 15 x+18=3(5 x+6) for every value of x.

4 -3 Equivalent Expressions Example 3: Writing Equivalent Expressions Write four equivalent expressions for each given expression. A. 9+15 3∙ 3+3∙ 5 Rewrite each term as a product 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. 25 m-5 m 5 m∙ 5 -5 m∙ 1 Rewrite each term as a product with GCF 5 m(5 -1) Apply the Distributive property 5 m∙ 4 Subtract 20 m Multiply

4 -3 Equivalent Expressions Continued: Example 3 C. 2(4 p+2) 2∙ 4 p+2∙ 2 Apply the Distributive property 8 p+4 Multiply 4+8 p Apply the Commutative property 4+23 p Write the coefficient of 8 as 23

4 -3 Equivalent Expressions You Try! Example 3 Write four equivalent expressions for each given expression. A. 3(9 p+3) B. 8+24 3∙ 9 p+3∙ 3 8∙ 1+8∙ 3 27 p+9 8(1+3) 9+27 p 8(3+1) 9+33 p 8(4)

4 -3 Equivalent Expressions Reflection CAN YOU write equivalent numerical and algebraic expressions?

4 -3 Equivalent Expressions Lesson Quiz Write four equivalent expressions for each given expression. 1. 20 - 8 2(10 -4); 4(5 -2); 4∙ 3; 12 2. 9 z + 12 3(3 z+4); 3(4+3 z); 32 z+12; 12+9 z

4 -3 Equivalent Expressions HOMEWORK