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Problem of the Day Becky plans to spend a total of 30 minutes doing chores before heading to the movies with her children. She plans to make the beds, clean the restroom, and wash dishes. She made the beds for 1/3 of the total time, washed dishes for ½ of the total time, and cleaned the restroom the remainder of the time. How much time did it take her to clean the restroom? 5 minutes

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**Learn to simplify algebraic expressions.**

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**In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms**

In the expression 7x + 9y + 15, 7x, 9y, and 15 are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by + and –. x 3 7x – 3y y + term term term term term In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. A variable by itself, like y, has a coefficient of 1. So y = 1y. Coefficient Variable 7 x

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**Like terms are terms with the same variable raised to the same power**

Like terms are terms with the same variable raised to the same power. The coefficients do not have to be the same. Constants, like 5, , and 3.2, are also like terms. 1 2 Like Terms Unlike Terms w 7 3x and 2x w and 5 and 1.8 5x2 and 2x 6a and 6b 3.2 and n Only one term contains a variable The exponents are different. The variables are different

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**Additional Example 1: Identifying Like Terms**

Identify like terms in the list. 3t 5w2 7t 9v w2 8v Look for like variables with like powers. Like terms: 3t and 7t 5w2 and 4w2 9v and 8v Use different shapes or colors to indicate sets of like terms. Helpful Hint

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Check It Out: Example 1 Identify like terms in the list. 2x 4y3 8x 5z y3 8z Look for like variables with like powers. Like terms: 2x and 8x 4y3 and 5y3 5z and 8z

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**+ = Combining like terms is like grouping similar objects. x x x x x x**

To combine like terms that have variables, add or subtract the coefficients.

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**Additional Example 2: Simplifying Algebraic Expressions**

Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 6t – 4t 6t – 4t 6t and 4t are like terms. 2t Subtract the coefficients. B. 45x – 37y + 87 In this expression, there are no like terms to combine.

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**Additional Example 2: Simplifying Algebraic Expressions**

Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6 Identify like terms. 3a2 + 5b + 11b2 – 4b + 2a2 – 6 Group like terms. 5a2 + b + 11b2 – 6 Add or subtract the coefficients.

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Check It Out: Example 2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 4x2 + 4y + 3x2 – 4y + 2x2 + 5 4x2 + 4y + 3x2 – 4y + 2x2 + 5 Identify like terms. Group like terms. Add or subtract the coefficients. 9x2 + 5

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**Simplify the expression**

Simplify the expression. Use the commutative and associative properties to help you. 8k2 + 4k – 3k2 + 3 – k + 5 8k2 + 4k – 3k2 + 3 – k + 5 Identify Like Terms Combine the terms

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**Simplify the expression**

Simplify the expression. Use the commutative and associative properties to help you. 10x3 + 5y2 + 2xy – 4y2 + 4xy – x3 10x3 + 5y2 + 2xy – 4y2 + 4xy – x3

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**Write an expression using the side lengths. x + 2x + 1 + 2x + 1**

Check It Out: Example 3 Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 1 2x + 1 x Write an expression using the side lengths. x + 2x x + 1 (x + 2x + 2x) + (1 + 1) Identify and group like terms. 5x + 2 Add the coefficients.

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**Write An Expression for the perimeter of the triangle.**

6v + s 5s – 4v 2s + 5 6v + s + 5s – 4v + 2s + 5 2v + 8s + 5

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