1. Page 12-17 Mr. Peter Richard’s Awesome Class!
1.5 Combining Like Terms
Page 12-17
Mr. Peter Richard’s Awesome Class!

2. Simplify Expression Simplify: Combine like terms
3 dogs + 3 cats + 5 dogs =
3d + 5c + 6d =
Like terms- because they both have d as a variable (Just add the coefficients # with the variable)
8 dogs + 3 cats
9d + 5c

3. Terms must match in variable and exponent
EXAMPLES
x 2x 3x -x x -3x
y 2y 3y -y y -3y
X2 2x x2 -x x x2
y2 2y y2 -y y y2

4. Simplify Each Expression
3x + 2x = 5x
8y – 2y + 5 =
6y + 5
8y – 2y = 6y
4k k =
2k + 17
4k – 2k = 2k
Watch the sign in front of the number!!!!

5. Simplify Each Expression
2b – 8 + 4b – 6b
-19 – 11a + a + 16 1
2b + 4b – 6b = 0b =
- 3 -8
-11a + a =
-10a
-10a - 3
b – 9b=
-8b
If there is no # in front of a variable it is a understood 1

6. Simplify the expression
A) Simplify the expression
6x + 5y² - y²=
4y² + 6x 1
5y² - 1y² = 4y²
B) Evaluate your answer for the given values
4y² + 6x
X = 5, y = 3
4(3)² + 6 (5)
4(9) + 6(5) = 66

7. Simplify the expression
A) Simplify the expression
5bc + 3c² + c²= 1
5bc + 4c²
3c² + 1c² = 4c²
B) Evaluate your answer for the given values
5bc + 4c²
b = 3, c = 2
5(3)(2) + 4(2)²
15(2) + 4(4) = 46

8. Simplifying with Distributive Property
Distributive Property: multiplying coefficient by what’s inside ( )’s to simplify
Example 3(5+6)
Distributive Property: Means to share the outside number with everything on the inside by multiplying
3 x 5 = 15
3 x 6 = 18 = 33
3(2x + 3)
3 x 2x = 6x
3 x 3 = 9
6x + 9

9. Simplifying with Distributive Property
3(2x + 4x²) + 5 (2x² + 5x)
3 ( 2x)= 6x +
5 ( 2x²)= 10x²
3 ( 4x²)= 12x² +
5 (5x) = 25x
6x + 12x² + 10x² + 25x =
22x² + 31x
Distributive Property: Means to share the outside number with everything on the inside by multiplying

10. Simplifying with Distributive Property
-2m - (2m -1) + 4m
-2m -1 (2m -1) + 4m
4(d + 3) + 7d
Don’t forget a negative times a negative makes a positive
4(d) + 4(3)
4d d
-2m -2m m
-4m m
4d + 7d = 11d
- 4m + 4m = 0m
11d + 12 1
Distributive Property: Means to share the outside number with everything on the inside by multiplying

11. Simplifying with Perimeter
Write the expression for the perimeter of the polygon shown.
Perimeter: Distance around an object 3
P = (x+4) (2x) + (2x+1)
(x+4)
Don’t forget to combine like terms
x + 2x +2x = 5x
(2x)
= 8
(2x+1)
5x + 8

12. Simplifying with Perimeter
Write the expression for the perimeter of the polygon shown.
Perimeter: Distance around an object
P = (2x+1) + (4x) + (3) + (6x+3)
(2x +1)
(4x)
Don’t forget to combine like terms
2x + 4x +6x = 12x
(3)
(6x + 3)
= 7
12x + 7

13. Lesson Quiz Combine like terms. 1. 3x + 4 + 2x 2. 13k + 6  8m + 9 + k
Simplify.
3. 4(3x + 6)  7x (x + 5) + 3x
Solve.
5. 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?
5x + 4
14k – 8m + 15
5x + 24
9x + 30 $3

14. Quiz Time!! Open Your books to Page 15 Quiz # 24, 28, 30, 32, 52
Homework # 23, 25, 27, 31, 51