1. Exercise
Simplify.
2(3 • 4)

2. Exercise
Simplify.
(5 x 3)6

3. Exercise
Simplify.
(4 + 10) + 7

4. Exercise
Simplify.
6 + (2 + 11)

5. Exercise
Simplify.
x(4 + 10)

6. Example 1
Simplify.
2(3n) = 6n

7. Example 2
Simplify.
(x + 2) + 9 =
x + 11

8. Constant
A constant is a number whose value does not change.

9. Term
A term is a constant, a variable, or the product of a constant and one or more variables. Terms are always separated from each other by a plus or minus sign.

10. Numerical Coefficient
A numerical coefficient is the number factor (constant) accompanying the variable in a term.

11. 3x + 2y − 4

12. Parts of an Expression 2x3y + 6
2 is the coefficient. x and y are variables. 3 is an exponent. 6 is a constant.

13. Example 3 Use the −6xy + − z to answer the following.2
Use the −6xy − z to answer the following.
What are the terms of the equation?
−6xy, , and −z x 2

14. Example 3 Use the −6xy + − z to answer the following.2
Use the −6xy − z to answer the following.
Does the expression have a constant term?
No. All terms contain a variable factor.

15. Example 3 Use the −6xy + − z to answer the following.2
Use the −6xy − z to answer the following.
What are the coefficients in the expression?
The coefficients are −6, , and −1. 1 2

16. Like Terms
Like terms are terms that have the same variable (or variables) with the same exponents.

17. Like Terms
5x, −7x, x
1 2
5xy2, −7xy2, 0.75xy2

18. Unlike Terms
4x, 4x2
6xy, −8xy3

19. 2y + 7y + 3y

20. Example 4
Simplify.
7x + 4x =
(7 + 4)x
= 11x

21. Example 5 Simplify. 2x + 7y + 3 – y + 5x = = (2x + 5x) + (7y – y) + 3

22. Exercise
Simplify.
5r + 8s − 2r + 3s
= 3r + 11s

23. Exercise
Simplify.
y + 11 − 5y + 4 − 3y
= −7y + 15

24. Exercise
Simplify.
6w − 8x − 2w + 3 − 4x
= 4w − 12x + 3

25. Exercise
Simplify.
−5a + 3z + 2a + 6z
= −3a + 9z

26. Exercise
Simplify.
8c + 5y − 2c + 9y
= 6c + 14y

27. Exercise
A rectangle has consecutive sides that are represented by x and x+3. Find the expression that represents the perimeter of the rectangle.

28. Exercise
The sides of a triangle are represented by x, 2x, and 2x − 5. Find the expression that represents its perimeter.

29. Exercise
A farmer has a rectangular pasture with dimensions x by 2x. If he places posts 15 ft. apart, how will he represent the distance between each post on the shorter side? on the longer side?

30. Exercise
Each side of a regular octagon (all sides equal in length) is represented by 14x. Find the expression that represents the perimeter of the regular octagon.

31. Exercise
The side of a square is 4 in. shorter than one side of a given rectangle. The side of the rectangle is represented by 2x + 3. Find the expression that represents the perimeter of the square.