SECTION 2-4Add and Subtract Variable Expressions

ESSENTIAL QUESTIONS

How are variable expressions simplified?

How are variable expressions evaluated?

Where you’ll see this:

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VOCABULARY1. Terms:

2. Like Terms:

3. Unlike Terms:

4. Simplify:

5. Combining Like Terms:

VOCABULARY1. Terms: The parts of a variable expression that are separated

by addition or subtraction signs

2. Like Terms:

3. Unlike Terms:

4. Simplify:

5. Combining Like Terms:

VOCABULARY1. Terms: The parts of a variable expression that are separated

by addition or subtraction signs

2. Like Terms: Have identical variable parts

3. Unlike Terms:

4. Simplify:

5. Combining Like Terms:

VOCABULARY1. Terms: The parts of a variable expression that are separated

by addition or subtraction signs

2. Like Terms: Have identical variable parts

3. Unlike Terms: Have different variable parts

4. Simplify:

5. Combining Like Terms:

VOCABULARY1. Terms: The parts of a variable expression that are separated

by addition or subtraction signs

2. Like Terms: Have identical variable parts

3. Unlike Terms: Have different variable parts

4. Simplify: Perform as many of the given operations as possible

5. Combining Like Terms:

VOCABULARY1. Terms: The parts of a variable expression that are separated

by addition or subtraction signs

2. Like Terms: Have identical variable parts

3. Unlike Terms: Have different variable parts

4. Simplify: Perform as many of the given operations as possible

5. Combining Like Terms: When you simplify and add or subtract like terms

EXAMPLE 1Add two terms to the list that are like terms.

a. 4x, 18x, -3.7x b. 17h2 , .98h2 , − 15h2

EXAMPLE 1Add two terms to the list that are like terms.

a. 4x, 18x, -3.7x b. 17h2 , .98h2 , − 15h2

Sample: x, 7x, -2x

EXAMPLE 1Add two terms to the list that are like terms.

a. 4x, 18x, -3.7x b. 17h2 , .98h2 , − 15h2

Sample: x, 7x, -2x Sample: h2 , 18h2 , − 4h2

EXAMPLE 2Simplify.

a. 3 x + 8 x b. 2x + 4x2 + (−3x ) + (−10x2 )

c. 7( x + y) + 4( x + y)

EXAMPLE 2Simplify.

a. 3 x + 8 x b. 2x + 4x2 + (−3x ) + (−10x2 )

c. 7( x + y) + 4( x + y)

11 x

EXAMPLE 2Simplify.

a. 3 x + 8 x b. 2x + 4x2 + (−3x ) + (−10x2 )

c. 7( x + y) + 4( x + y)

11 x −6x2 − x

EXAMPLE 2Simplify.

a. 3 x + 8 x b. 2x + 4x2 + (−3x ) + (−10x2 )

c. 7( x + y) + 4( x + y)

11 x −6x2 − x

11( x + y)

EXAMPLE 2Simplify.

a. 3 x + 8 x b. 2x + 4x2 + (−3x ) + (−10x2 )

c. 7( x + y) + 4( x + y)

11 x −6x2 − x

11( x + y)

11x + 11 y

EXAMPLE 3Simplify.

a. .1m − 1.1m b. 7 y + 4x − 7 y − 3x

c. 12x2 + 3 y − 6x2 − 2 y − 6x2

EXAMPLE 3Simplify.

a. .1m − 1.1m b. 7 y + 4x − 7 y − 3x

c. 12x2 + 3 y − 6x2 − 2 y − 6x2

−m

EXAMPLE 3Simplify.

a. .1m − 1.1m b. 7 y + 4x − 7 y − 3x

c. 12x2 + 3 y − 6x2 − 2 y − 6x2

−m x

EXAMPLE 3Simplify.

a. .1m − 1.1m b. 7 y + 4x − 7 y − 3x

c. 12x2 + 3 y − 6x2 − 2 y − 6x2

−m x

y

SOME IMPORTANT IDEAS

SOME IMPORTANT IDEAS

Compare variable parts

SOME IMPORTANT IDEAS

Compare variable parts

Work alphabetically, then highest power

SOME IMPORTANT IDEAS

Compare variable parts

Work alphabetically, then highest power

Simplify first, then evaluate

EXAMPLE 4Evaluate each expression when x = 2 and y = -3.

a. 6x2 + 3x2 b. 3x2 − y − x2

EXAMPLE 4Evaluate each expression when x = 2 and y = -3.

a. 6x2 + 3x2 b. 3x2 − y − x2

9x2

EXAMPLE 4Evaluate each expression when x = 2 and y = -3.

a. 6x2 + 3x2 b. 3x2 − y − x2

9x2

9(2)2

EXAMPLE 4Evaluate each expression when x = 2 and y = -3.

a. 6x2 + 3x2 b. 3x2 − y − x2

9x2

9(2)2

9(4)

EXAMPLE 4Evaluate each expression when x = 2 and y = -3.

a. 6x2 + 3x2 b. 3x2 − y − x2

9x2

9(2)2

9(4)

36

EXAMPLE 4Evaluate each expression when x = 2 and y = -3.

a. 6x2 + 3x2 b. 3x2 − y − x2

9x2

9(2)2

9(4)

36

2x2 − y

EXAMPLE 4Evaluate each expression when x = 2 and y = -3.

a. 6x2 + 3x2 b. 3x2 − y − x2

9x2

9(2)2

9(4)

36

2x2 − y

2(2)2 − (−3)

EXAMPLE 4Evaluate each expression when x = 2 and y = -3.

a. 6x2 + 3x2 b. 3x2 − y − x2

9x2

9(2)2

9(4)

36

2x2 − y

2(2)2 − (−3)

8 + 3

EXAMPLE 4Evaluate each expression when x = 2 and y = -3.

a. 6x2 + 3x2 b. 3x2 − y − x2

9x2

9(2)2

9(4)

36

2x2 − y

2(2)2 − (−3)

8 + 3

11

EXAMPLE 4

c. x2 − 4 y − 2x2 + y

Evaluate each expression when x = 2 and y = -3.

EXAMPLE 4

c. x2 − 4 y − 2x2 + y

−x2 − 3 y

Evaluate each expression when x = 2 and y = -3.

EXAMPLE 4

c. x2 − 4 y − 2x2 + y

−x2 − 3 y

−(2)2 − 3(−3)

Evaluate each expression when x = 2 and y = -3.

EXAMPLE 4

c. x2 − 4 y − 2x2 + y

−x2 − 3 y

−(2)2 − 3(−3)

−4 + 9

Evaluate each expression when x = 2 and y = -3.

EXAMPLE 4

c. x2 − 4 y − 2x2 + y

−x2 − 3 y

−(2)2 − 3(−3)

−4 + 9

5

Evaluate each expression when x = 2 and y = -3.

PROBLEM SET

PROBLEM SET

p. 68 #1-43 odd, skip #13

“Use what talents you possess: the woods would be very silent if no birds sang except those that sang best.” - Henry Van

Dyke