1. Simplifying Expressions (XEI303): Combining Like Terms Name Nov 21, 2011 1. Key Terms Key TermDefinition Base The number that is going to be raised to a power. Example: in 8 2, 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; 8 2 = 8 × 8 = 64 Coefficient A number or symbol multiplied with a variable in an algebraic term Example: 4 in the term 4x

2. 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

3. 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 = 5g5 = 5 5g + 5 Step 1 Step 2 Step 3

4. 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 + - 10m Negative sign belongs to the 10m

5. 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 + 1x Don’t forget the “hidden 1”

6. 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”

7. 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 + 7 Don’t forget the “the “plus negative”

8. 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