1. Objectives
Simplify expressions with several variables by combining like terms.

2. Glossary Terms Coefficient Variable Exponent Term Like Terms
Simplified

3. Some Things to Remember
Just Watch What Happens x 1x
+1x1 1
+1x
+1x1

4. Like Terms – same variable with same exponent
Key Skills
Like Terms – same variable with same exponent
Simplify
When combining like terms, only use the coefficients.
6x + 2x =
6x + 2x = 8x
Simplify
4x + 3y – 2x + 4y =
2x + 7y
Never, NEVER, combine x’s and y’s or constant terms with variable terms. 2x + 7y ≠ 9xy and 3a + 6 ≠ 9a.

5. + 7x 7x + 3y + 3y + 5y + 5y – 9x – 9x – 17y – 17y = – 2x – 2x = – 9y
Just Watch What Happens
+ 7x 7x
+ 3y
+ 3y
+ 5y
+ 5y
– 9x
– 9x
– 17y
– 17y
= – 2x
– 2x
= – 9y
– 9y

6. 3 + 5x = 3 + 5x ≠ 8x 3(5x) = 15x TRY THESE 1) 3q + 7q = 10q
Your welcome
2) 4x + 8y – 10x + 3y =
4x + 8y – 10x + 3y =
– 6x + 11y
Review Again
3 + 5x = 3 + 5x
≠ 8x
3(5x) =
15x

7. In algebraic terms, find the perimeter of the following shape.
4x + 3y
Key Skills
3x – 2y
3x – 2y 2x
To find the perimeter, add the sides together.
P = 3x – 2y + 2x + 3x – 2y + 4x + 3y =
12x – y
What is the perimeter if x = 5 and y = 8?
P = 12(5) – 8 = 52

8. Find the perimeter of the following shape when x = 2.
TRY THIS
5x + y
5x + y
6x – 2y
To find the perimeter, add the sides together.
P = 5x + y + 5x + y + 6x – 2y =
16x = 32
Does the value of y matter in this problem?
Obviously Not!

9. A farmer has two rectangular fields.
TRY THIS
He wants to put a fence around both. In algebraic terms, how much fence would he need?
3x – 6
2x + 5
Field 2 4
Field 1 3
P1 = x x + 5
P2 = x – 6 + 3x – 6
P1 = 4x + 16
P2 = 6x – 4
How much fence would the farmer need if x = 5?
Ptotal = 4x x – 4
Ptotal = 10x + 12
Ptotal = 10(5) + 12
Ptotal = 62

10. “Your Turn” 7t – 4t = 24 6y – 8y – y = 27 -3s + 8s – 10s = 35
18a – 14a = 36
-5x + 7x – 10x = 48
10z + 2z – 13z = 45
-12r + 15r = 21
-3b – 5b – 2b = 80