i can factor numerical expressions. i can factor algebraic expressions

4-3 Equivalent Expressions

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


Vocabularyterm coefficientequivalent expressions

4-3 Equivalent ExpressionsThe 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.

You can use the greatest common factor (GCF) and the Distributive Property to factor numerical expressions.

In the term 4x, 4 is called the coefficient. A coefficient is the number that is multiplied by a variable in an algebraic expression.


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

Remember!

4-3 Equivalent ExpressionsExample 1: Factoring Numerical Expressions

A. Factor the sum of terms as a product of the GCF and a sum.

27+39

3(9+13)

The terms are 27 and 39The GCF of the terms is 3Rewrite each term as a product with GCF

39+3∙13

Apply the distributive property

4-3 Equivalent ExpressionsExample 1: Factoring Numerical Expressions

B. Factor the sum of terms as a product of the GCF and a sum.

35+15

5(7+3)

The terms are 35 and 15

The GCF of the terms is 5Rewrite each term as a product with GCF

5∙7+5∙3


4-3 Equivalent ExpressionsYou Try! Example 1

Factor the sum of terms as a product of the GCF and a sum.

A. 14+42

14(1+3)14∙1+14∙3

B. 20+564∙5+4∙144(5+14)

4-3 Equivalent ExpressionsExample 2: Factoring Algebraic Expressions

A. Factor the sum of terms as a product of the GCF and a sum.

12b + 28

4∙3b + 4∙7

4(3b+7)

The terms are 12b and 28

The GCF of the terms is 4Rewrite each term as a product with GCFApply the distributive property

4-3 Equivalent ExpressionsExample 2: Factoring Algebraic Expressions

B. Factor the sum of terms as a product of the GCF and a sum.

16b+32

16(b+2)

The terms are 16b and 32The GCF of the terms is 16Rewrite each term as a product with GCF

16∙b+16∙2



Factor the sum of terms as a product of the GCF and a sum.

A. 12b+28

4(3b+7)4∙3b+4∙7

B. 40y30y

10y∙410y∙310y(43)


Reflection

CAN YOU factor numerical and algebraic expressions?

4-3 Equivalent ExpressionsLesson Quiz

Factor the sum of terms as a product of the GCF and a sum

15(3+1)1. 45 + 152. 24 + 40 8(3+5)

4(4y+9)

30(3+2s)

3. 16y + 36

4. 90 + 60s

4-3 Equivalent ExpressionsHOMEWORK

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.

4-3 Equivalent ExpressionsExample 3: Writing Equivalent Expressions

Write four equivalent expressions for each given expression.

A. 9+15

3(3+5)

3∙3+3∙5

3(5+3)3(8)

Rewrite each term as a product with GCF

Apply the Commutative property

Apply the Distributive property

Add


Continued: Example 3

B. 25m-5m

5m(5-1)

5m∙5-5m∙1

5m∙420m

Rewrite each term as a product with GCF

Subtract


Multiply


C. 2(4p+2)

8p+42∙4p+2∙2

4+8p

4+23p


Apply the Commutative property

Multiply

Write the coefficient of 8 as 23

Continued: Example 3



A. 3(9p+3)

27p+93∙9p+3∙3

9+27p9+33p

B. 8+24

8(4)8(3+1)8(1+3)8∙1+8∙3


Reflection

CAN YOU write equivalent numerical and algebraic expressions?

4-3 Equivalent ExpressionsLesson Quiz

1. 20 - 8

2. 9z + 12

2(10-4); 4(5-2); 4∙3; 12

3(3z+4); 3(4+3z); 32z+12; 12+9z


4-3 Equivalent ExpressionsHOMEWORK

p. 158: 13-18, 31-36

HOMEWORK

p. 158: 13-18, 31-36

i can factor numerical expressions. i can factor algebraic expressions

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