I CAN factor numerical expressions. I CAN factor algebraic expressions I CAN factor numerical expressions. I CAN factor algebraic expressions. I CAN write equivalent numerical and algebraic expressions.

Vocabulary term coefficient equivalent expressions

The terms of an expression are the parts of the expression that are added or subtracted. The terms of the expression 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 an algebraic expression. You can use the greatest common factor (GCF) and the Distributive Property to factor numerical expressions.

The greatest common factor (GCF) is the largest common factor of two or more given numbers. Remember!

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 3∙9+3∙13 Rewrite each term as a product with GCF 3(9+13) Apply the distributive property

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

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

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

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

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

Reflection CAN YOU factor numerical and algebraic expressions?

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

HOMEWORK p. 158: 1-12, 19-21, 25-27

There are many other ways to write equivalent expressions for each of the expressions in Example 3. Helpful Hint

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.

Example 3: Writing Equivalent Expressions Write four equivalent expressions for each given expression. A. 9+15 Rewrite each term as a product with GCF 3∙3+3∙5 3(3+5) Apply the Distributive property 3(5+3) Apply the Commutative property 3(8) Add

Continued: Example 3 B. 25m-5m Rewrite each term as a product with GCF 5m∙5-5m∙1 5m(5-1) Apply the Distributive property 5m∙4 Subtract 20m Multiply

Continued: Example 3 C. 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

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

Reflection CAN YOU write equivalent numerical and algebraic expressions?

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

HOMEWORK HOMEWORK p. 158: 13-18, 31-36 p. 158: 13-18, 31-36