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Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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Warm Up Find the GCF of each set of numbers. 1. 12 and , 45 and 30 2. 18 and , 24 and 30 5. 72, 80 and 96 2 15 6 2 8

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Problem of the Day Erin takes half of the cherries from a bowl. Then her brother takes half of the remaining cherries. Finally, Diego takes 3 of the remaining cherries. This leaves 4 cherries in the bowl. How many cherries were in the bowl to start? 28 cherries

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I can factor numerical and algebraic expressions and write equivalent numerical and algebraic expression.

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Vocabulary term coefficient equivalent expressions

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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.

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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.

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**The greatest common factor (GCF) is the largest**

common factor of two or more given numbers. Remember!

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**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 The GCF of the terms is 3 Rewrite each term as a product with GCF 3(9+13) Apply the distributive law

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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 The GCF of the terms is 15 Rewrite each term as a product with GCF 15(1+3) Apply the Distributive property

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**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 Rewrite each term as a product with GCF 4.3b + 4.7 4(3b+7) Apply the Distributive law

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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 b The GCF of the terms is Rewrite each term as a product with GCF 16.b+16.2 16(b+2) Apply the distributive property

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

Helpful Hint

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**Additional Example 3: Writing Equivalent Expressions**

Write four equivalent expressions for each given expression. A 9+15 The terms are 9 and 15 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

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

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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

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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

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Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

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**Continued: Lesson Quiz**

Write four equivalent expressions for each given expression. 2(10-4); 4(5-2); 4.3; 12 6. 9z + 12 3(3z+4); 3(4+3z); 32z+12; 12+9z

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**Lesson Quizzes Lesson Quiz for Student Response Systems**

1. Factor the sum of terms as a product of the GCF and a sum 60+30 A. 60(1+2) B. 90 C. 30(2) D. 30(2+1)

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**Continued: Lesson Quiz for Student Response Systems**

2. Factor the sum of terms as a product of the GCF and a sum 13+39r A. 13(1+3r) B. 13(1+3) C. 13(3r) D. 42r

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**Continued: Lesson Quiz for Student Response Systems**

3. Which expression is not equivalent to 12-3? A. 3(4-1) B. 3(22-1) C D. 3(1-3)

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**Continued: Lesson Quiz for Student Response Systems**

4. Which expression is not equivalent to 8z+12? A. 8z+4.3 B. 4(2z+3) C. 4(2z+12) D. 4(3+2z)

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