11-1 Simplifying Algebraic Expressions

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpSimplify.

2011

8

3

Course 3

11-1 Simplifying Algebraic Expressions

4. 17 + 8 20 23. 6 + 9 10 + 3

2. 16 8 + 4 11. 9 + 13 5 + 3

Problem of the Day

Ray and Katrina are wandering through the wildlife preserve. They observe and count a total of 15 wild turkeys and deer and a total of 46 legs. How many of each did they see? 7 turkeys, 8 deer

11-1 Simplifying Algebraic Expressions

Learn to combine like terms in an expression.

11-1 Simplifying Algebraic Expressions

Vocabularytermlike termequivalent expressionsimplify

11-1 Simplifying Algebraic Expressions

Terms in an expression are separated by plus or minus signs.

Like terms can be grouped together because they have the same variable raised to the same power.

Equivalent expressions have the same value for all values of the variables.

11-1 Simplifying Algebraic Expressions

Constants such as 4, 0.75, and 11 are like terms because none of them have a variable.

Helpful Hint

Combine like terms.

Additional Example 1: Combining Like Terms To Simplify

Identify like terms.

Combine coefficients: 14 – 5 = 9

A. 14a – 5a

9a

B. 7y + 8 – 3y – 1 + y Identify like terms ; the coefficient of y is 1, because 1y = y.

Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7

5y + 7

11-1 Simplifying Algebraic Expressions

Combine like terms.

Additional Example 2A: Combining Like Terms in Two-Variables Expressions

Identify like terms.

Combine coefficients: 9 – 2 = 7

9x + 3y – 2x + 5

7x + 3y + 5

9x + 3y – 2x + 5

11-1 Simplifying Algebraic Expressions

Combine like terms.

Additional Example 2B: Combining Like Terms in Two-Variable Expressions

Identify like terms.

Combine coefficients: 5 – 2 = 3 and 7 – 3= 4

5t + 7p – 3p – 2t

3t + 4p

5t + 7p – 3p – 2t

11-1 Simplifying Algebraic Expressions

Combine like terms.

Additional Example 2C: Combining Like Terms in Two-Variable Expressions

No like terms.

4m + 9n – 2

4m + 9n – 2

11-1 Simplifying Algebraic Expressions

To simplify an expression, perform all possible operations, including combining like terms.

11-1 Simplifying Algebraic Expressions

The Distributive Property states that a(b + c) = ab + ac for all real numbers a, b, and c. For example, 2(3 + 5) = 2(3) + 2(5).

Remember!

Simplify 6(5 + n) – 2n.

Additional Example 3: Using the Distributive Property to Simplify

Distributive Property.

Multiply.

6(5 + n) – 2n

30 + 6n – 2n

6(5) + 6(n) – 2n

30 + 4n Combine coefficients 6 – 2 = 4.

11-1 Simplifying Algebraic Expressions

Solve x + 3x = 48.

Additional Example 4: Combining Like Terms to Solve Algebraic Equations

Identify like terms. The coefficient of x is 1.

Combine coefficients: 1 + 3 = 4

x + 3x = 48

4x = 48

4x = 48

x = 12

Divide both sides by 4.4 4

11-1 Simplifying Algebraic Expressions

Lesson Quiz

Combine like terms.

1. 3x + 4 + 2x 2. 13k + 6 8m + 9 + k

Simplify.

3. 4(3x + 6) 7x 4. 6(x + 5) + 3x

Solve.

5. 6y + y = 42

6. The accounting department ordered 15 boxes of pens. The marketing department ordered 9 boxes of pens. If the total cost of the combined order was $72, what is the price of each box of pens?

14k – 8m + 15

y = 6

5x + 4

5x + 24 9x + 30

$3

11-1 Simplifying Algebraic Expressions