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Factoring and Writing Equivalent Expressions

Learn how to factor numerical and algebraic expressions and write equivalent expressions using the greatest common factor (GCF) and the distributive property.

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Factoring and Writing Equivalent Expressions

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  1. WarmUp Problem of the Day Lesson Presentation Lesson Quizzes

  2. Warm Up Find the GCF of each set of numbers. 1. 12 and 50 3. 30, 45 and 30 2. 18 and 30 4. 16, 24 and 30 5. 72, 80 and 96 2 15 6 2 8

  3. 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

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

  5. Vocabulary term coefficient equivalent expressions

  6. 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.

  7. 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.

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

  9. 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

  10. 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

  11. 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

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

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

  14. 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 with GCF 3.3+3.5 3(3+5) Apply the Distributive property 3(5+3) Apply the Commutative property 3(8) Add

  15. 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

  16. Continued: Example 3 C. 2(4p+2) 2(4p+2) Apply the Distributive property 2.4p+2.2 8p+4 Multiply 4+8p Apply the Commutative property 4+23p Write the coefficient of 8 as 23

  17. Check It Out: Example 3 Write four equivalent expressions for each given expression. 3(9p+3) 3(9p+3) Apply the Distributive property 3.9p+3.3 27p+9 Multiply 9+27p Apply the Commutative property 9+33p Write the coefficient of 27 as 33

  18. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

  20. Continued: Lesson Quiz Write four equivalent expressions for each given expression. 5. 20 - 8 2(10-4); 4(5-2); 4.3; 12 6. 9z + 12 3(3z+4); 3(4+3z); 32z+12; 12+9z

  21. 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)

  22. 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

  23. 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. 3.4-3 D. 3(1-3)

  24. 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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