Simplifying Expressions 1-7 Simplifying Expressions Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 1

Warm Up Add. 1. 427 + 35 462 2. 1.06 + 0.74 1.80 3. 10 Multiply. 4. 25(8) 200 5. 1.3(22) 28.6 6.

Objectives Use the Commutative, Associative, and Distributive Properties to simplify expressions. Combine like terms.

Vocabulary term like terms coefficient

The Commutative and Associative Properties of Addition and Multiplication allow you to rearrange an expression to simplify it.

Example 1A: Using the Commutative and Associative Properties Simplify. Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 11(5) 55

Example 1B: Using the Commutative and Associative Properties Simplify. 45 + 16 + 55 + 4 45 + 55 + 16 + 4 Use the Commutative Property. (45 + 55) + (16 + 4) Use the Associative Property to make groups of compatible numbers. (100) + (20) 120

Compatible numbers help you do math Helpful Hint Compatible numbers help you do math mentally. Try to make multiples of 5 or 10. They are simpler to use when multiplying.

Check It Out! Example 1a Simplify. Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 21

Check It Out! Example 1b Simplify. 410 + 58 + 90 + 2 410 + 90 + 58 + 2 Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. (410 + 90) + (58 + 2) (500) + (60) 560

( ) Check It Out! Example 1c Simplify. 1 2 7 • 8 1 2 8 • 7 Use the Commutative Property. ( ) 1 2 • 8 7 Use the Associative Property to make groups of compatible numbers. 4 • 7 28

The Distributive Property is used with Addition to Simplify Expressions. The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.

Example 2A: Using the Distributive Property with Mental Math Write the product using the Distributive Property. Then simplify. 5(59) 5(60 – 1) Rewrite 59 as 60 - 1. 5(60) – 5(1) Use the Distributive Property. 300 – 5 Multiply. 295 Subtract.

Example 2B: Using the Distributive Property with Mental Math Write the product using the Distributive Property. Then simplify. 8(33) 8(30 + 3) Rewrite 33 as 30 + 3. 8(30) + 8(3) Use the Distributive Property. 240 + 24 Multiply. 264 Add.

Check It Out! Example 2a Write the product using the Distributive Property. Then simplify. 9(52) 9(50 + 2) Rewrite 52 as 50 + 2. 9(50) + 9(2) Use the Distributive Property. 450 + 18 Multiply. 468 Add.

Check It Out! Example 2b Write the product using the Distributive Property. Then simplify. 12(98) 12(100 – 2) Rewrite 98 as 100 – 2. 12(100) – 12(2) Use the Distributive Property. 1200 – 24 Multiply. 1176 Subtract.

Check It Out! Example 2c Write the product using the Distributive Property. Then simplify. 7(34) 7(30 + 4) Rewrite 34 as 30 + 4. 7(30) + 7(4) Use the Distributive Property. 210 + 28 Multiply. 238 Add.

The terms of an expression are the parts to be added or subtracted The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. Like terms Constant 4x – 3x + 2

A coefficient is a number multiplied by a variable A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1. Coefficients 1x2 + 3x

Using the Distributive Property can help you combine like terms Using the Distributive Property can help you combine like terms. You can factor out the common factors to simplify the expression. 7x2 – 4x2 = (7 – 4)x2 Factor out x2 from both terms. = (3)x2 Perform operations in parenthesis. = 3x2 Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.

Example 3A: Combining Like Terms Simplify the expression by combining like terms. 72p – 25p 72p – 25p 72p and 25p are like terms. 47p Subtract the coefficients.

Example 3B: Combining Like Terms Simplify the expression by combining like terms. A variable without a coefficient has a coefficient of 1. and are like terms. Write 1 as . Add the coefficients.

Example 3C: Combining Like Terms Simplify the expression by combining like terms. 0.5m + 2.5n 0.5m + 2.5n 0.5m and 2.5n are not like terms. 0.5m + 2.5n Do not combine the terms.

Check It Out! Example 3 Simplify by combining like terms. 3a. 16p + 84p 16p + 84p 16p + 84p are like terms. 100p Add the coefficients. 3b. –20t – 8.5t –20t – 8.5t −20t and 8.5t are like terms. –28.5t Subtract the coefficients. 3c. 3m2 + m3 3m2 + m3 3m2 and m3 are not like terms. 3m2 + m3 Do not combine the terms.

Example 4: Simplifying Algebraic Expressions Simplify 14x + 4(2 + x). Justify each step. Procedure Justification 1. 14x + 4(2 + x) 2. 14x + 4(2) + 4(x) Distributive Property 3. 14x + 8 + 4x Multiply. Commutative Property 4. 14x + 4x + 8 5. (14x + 4x) + 8 Associative Property 6. 18x + 8 Combine like terms.

Check It Out! Example 4a Simplify 6(x – 4) + 9. Justify each step. Procedure Justification 1. 6(x – 4) + 9 2. 6(x) – 6(4) + 9 Distributive Property 3. 6x – 24 + 9 Multiply. Combine like terms. 4. 6x – 15

Check It Out! Example 4b Simplify −12x – 5x + 3a + x. Justify each step. Procedure Justification 1. –12x – 5x + 3a + x 2. –12x – 5x + x + 3a Commutative Property 3. –16x + 3a Combine like terms.

Lesson Quiz: Part I Simplify each expression. 1. 165 +27 + 3 + 5 200 2. 8 Write each product using the Distributive Property. Then simplify. 3. 5($1.99) 5($2) – 5($0.01) = $9.95 4. 6(13) 6(10) + 6(3) = 78

Lesson Quiz: Part II Simplify each expression by combining like terms. Justify each step with an operation or property. 5. 6. 14c2 – 9c 14c2 – 9c 7. 301x – x 300x 8. 24a + b2 + 3a + 2b2 27a + 3b2