Simplifying Expressions (XEI303):Combining Like Terms

Name

Nov 21, 2011

1. Key Terms

Key Term Definition

Base The number that is going to be raised to a power.

Example: in 82, 8 is the base

Exponent The exponent of a number shows you how many times the number is to be used in a multiplication.

Example: Exponent is 2; 82 = 8 × 8 = 64

Coefficient

A number or symbol multiplied with a variable in an algebraic term

Example: 4 in the term 4x

Simplifying Expressions (XEI303):Combining Like Terms

Name

Nov 21, 2011

2. What are Combining Like Terms?

1. What are like terms?• They have the same variable as a base• Constants have no variable (0 exponent)• For now, all bases will have exponent of 1

2. How do I combine like terms?1. Circle, square, underline like terms

• Positive/negative sign before belongs to the number (include it in the circle)• Turn all minus signs into a “plus negative”

• A variable by itself has a “hidden” coefficient of 1

2. Combine like terms (DON’T CHANGE EXPONENT)3. Add unlike terms for final simplified answer

Simplifying Expressions (XEI303):Combining Like Terms

Name

Nov 21, 2011

3. Examples:

Combining Like Terms

Example 1: Simplify by combining like terms

2g + 5 + 3g

I DO

1. Like terms have the same base; circle/square/underline like terms (including the sign)

2. Combine like terms (DON’T CHANGE EXPONENT)

3. Add unlike terms for final simplified answer

2g + 3g = 5g 5 = 5

5g + 5

Step 1

Step 2

Step 3

Simplifying Expressions (XEI303):Combining Like Terms

Name

Nov 21, 2011

2. Examples:

Combining Like Terms

Example 2: Simplify by combining like terms

6m – 10m

I DO

• Turn all minuses into a “plus negative”

6m + -10m = -4m

-4m

Step 1

Step 2

Step 3

6m + -10mNegative sign

belongs to the 10m

Simplifying Expressions (XEI303):Combining Like Terms

Name

Nov 21, 2011

2. Examples:

Combining Like Terms

Example 3: Simplify by combining like terms

3x – 5 + x

I DO

• Put a coefficient of 1 in front of a variable by itself (Note: -x = -1x)

3x + 1x = 4x -5 = -5

4x + -5

Step 1

Step 2

Step 3

3x + -5 + 1xDon’t forget the

“hidden 1”

Simplifying Expressions (XEI303):Combining Like Terms

Name

Nov 21, 2011

2. Examples:

Combining Like Terms

Example 4: Simplify by combining like terms

-r – 8r

WE DO

-1r + -8r = -9r

-9r

Step 1

Step 2

Step 3

-1r + -8r

Don’t forget the “hidden 1” or the “plus negative”

Simplifying Expressions (XEI303):Combining Like Terms

Name

Nov 21, 2011

2. Examples:

Combining Like Terms

Example 5: Simplify by combining like terms

3x – 5 – 5x + 7

WE DO

3x + -5x = -2x -5 + 7 = 2

-2x + 2

Step 1

Step 2

Step 3

3x + -5 + -5x + 7Don’t forget the “the

“plus negative”

Simplifying Expressions (XEI303):Combining Like Terms

Name

Nov 21, 2011

2. Examples:

Combining Like Terms

Example 6: You are trying to find the perimeter of a sandbox. Perimeter is found by adding up the length of all sides. The width is x + 5 feet and the length is 2x + 2 feet. Write and simplify an expression for the perimeter of the sandbox.

WE DO

2X + 2 ft

X + 5 ft

2X + 2 ft

X + 5 ft

2x + 2 + 2x + 2 + 1x + 5 + 1x + 5

2x + 2x + 1x + 1x = 6x

2 + 2 + 5 + 5 = 14

6x + 14 feet