4-3 Equivalent Expressions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

4-3 Equivalent Expressions Do Now Find the GCF of each set of numbers and and and , 24 and , 80 and

4-3 Equivalent Expressions SWBAT factor numerical and algebraic expressions and write equivalent numerical and algebraic expression.

4-3 Equivalent Expressions Vocabulary term coefficient equivalent expressions

4-3 Equivalent Expressions The terms of an expression are the parts that are added or subtracted. The terms of the expressions 140+4x are 140 and 4x. In the term 4x, the 4 is called the coefficient. A coefficient is the number that is multiplied by a variable.

4-3 Equivalent Expressions Equivalent expressions are expressions that have the same value as one another but are written differently. The expressions 15x+18 and 3(5x+6) are equivalent expressions. 15x+18=3(5x+6) because of the Distributive Property. You can use the greatest common factor (GCF) and the Distributive Property to factor numerical expressions.

4-3 Equivalent Expressions Ex. 1 Factor the sum of terms as a product of the GCF and a sum. 3( ) (9+13) The terms are 27 and 39 The GCF of the terms is 3, so place 3 on the outside of the parenthesis Now write the remaining factors inside of the parenthesis

4-3 Equivalent Expressions Goals for factoring expressions 1.Identify the terms 2. Find the GCF –Place it outside of the parenthesis 3. Determine the remaining factors –Place them inside of the parenthesis

4-3 Equivalent Expressions Ex. 2 Factor the sum of terms as a product of the GCF and a sum ( ) (1+3) Goals for factoring expressions 1. Identify the terms 2. Find the GCF –Place it outside of the parenthesis 3. Determine the remaining factors –Place them inside of the parenthesis

4-3 Equivalent Expressions Ex. 3 Factor the sum of terms as a product of the GCF and a sum. 12b ( ) 12b (3b+7) 443b 7 Goals for factoring expressions 1. Identify the terms 2. Find the GCF –Place it outside of the parenthesis 3. Determine the remaining factors –Place them inside of the parenthesis

4-3 Equivalent Expressions Ex. 4 Factor the sum of terms as a product of the GCF and a sum. 16b+32 16(b+2)

4-3 Equivalent Expressions There are many other ways to write equivalent expressions for each of the expressions in Example 3. Helpful Hint

4-3 Equivalent Expressions Ex. 5 Write 3 equivalent expressions for each given expression. A (3+5) 3( ) 3(8) 24

4-3 Equivalent Expressions The 3 expressions 1 st expression –Factored Form 2 nd expression –Combine the terms inside of the parenthesis 3 rd expression –Multiply

4-3 Equivalent Expressions Ex. 6 B. 25m-5m 25m-5m 5m(5 – 1) 5m( ) 5m(4) 20m The terms are 25m and 1m 1 st Form 2 nd Form 3 rd Form

4-3 Equivalent Expressions C. 2(4p+2) Ex. 7

4-3 Equivalent Expressions Ex. 8 Write three equivalent expressions for each given expression. 3(9p+3)

4-3 Equivalent Expressions Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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

4-3 Equivalent Expressions Continued: Lesson Quiz z (5-2); 4.3; 12 3(3z+4) Write all equivalent expressions for each given expression.

4-3 Equivalent Expressions Lesson Quiz for Student Response Systems 1. Factor the sum of terms as a product of the GCF and a sum Lesson Quizzes