Equivalent Expressions Warm Up Find the GCF of

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

Equivalent Expressions Learn factor numerical and algebraic expressions and write equivalent numerical and algebraic expression.

Equivalent Expressions Vocabulary term coefficient equivalent expressions

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

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.

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

Equivalent Expressions Additional Example 1: Factoring Numerical Expressions Factor the sum of terms as a product of the GCF and a sum. 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

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

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

Equivalent Expressions Check It Out: Example 2 Factor the sum of terms as a product of the GCF and a sum. 16 b+32 The terms are 16 b and 32 2. 2. b+2. 2. 2 The GCF of the terms is 2. 2 16. b+16. 2 Rewrite each term as a product with GCF 16(b+2) Apply the distributive property

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

Equivalent Expressions Additional Example 3: Writing Equivalent Expressions Write four equivalent expressions for each given expression. A. 9+15 The terms are 9 and 15 9+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

Equivalent Expressions Continued: Example 3 B. 25 m-5 m The terms are 25 m and 1 m 5. 5 m-1. 5 m Rewrite each term as a product with common factor 5 m (5 -1)5 m Apply the Distributive property 4. 5 m Subtract 20 m Multiply

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

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

Equivalent Expressions Lesson Quizzes Standard Lesson Quiz for Student Response Systems

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

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

Equivalent Expressions 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)

Equivalent Expressions Continued: Lesson Quiz for Student Response Systems 2. Factor the sum of terms as a product of the GCF and a sum 13+39 r A. 13(1+3 r) B. 13(1+3) C. 13(3 r) D. 42 r

Equivalent Expressions 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)

Equivalent Expressions Continued: Lesson Quiz for Student Response Systems 4. Which expression is not equivalent to 8 z+12? A. 8 z+4. 3 B. 4(2 z+3) C. 4(2 z+12) D. 4(3+2 z)