1. Section 1 Algebraic Expressions And Formulas
Algebra 2 A Chapter 1
Section 1
Algebraic Expressions
And Formulas

2. Algebraic Expressions
ALGEBRA 2 LESSON 1-1
Use the order of operations to simplify each expression.
1. 8 • 3 – 2 • 4
2. 8 – ÷ 3
3. 24 ÷ 12 • 4 ÷ 3
4. 3 • ÷ 4
÷ 9 –
6. ( ) ÷ 8 – (23 + 1)

3. Algebraic Expressions
ALGEBRA 2 LESSON 1-1
1. 8 • 3 – 2 • 4 = (8 • 3) – (2 • 4) = 24 – 8 = 16
2. 8 – ÷ 3 = 8 – 4 + (6 ÷ 3) = 8 – = (8 – 4) + 2 = = 6
÷ 12 • 4 ÷ 3 = (24 ÷ 12) • 4 ÷ 3 = 2 • 4 ÷ 3 = (2 • 4) ÷ 3 = 8 ÷ 3 = or 2
4. 3 • ÷ 4 = 3 • ÷ 4 + (3 • 64) + (12 ÷ 4) = = 195
÷ 9 – = ÷ 9 – = 27 + (18 ÷ 9) – = – = (27 + 2) – = 29 – = (29 – 9) + 1 = = 21
6. ( ) ÷ 8 – (23 + 1) = ( ) ÷ 8 – (8 + 1) = 64 ÷ 8 – 9 = (64 ÷ 8) – 9 = 8 – 9 = –1
Solutions 8 3 2 3

4. Evaluating Algebraic Expressions
Variable – a symbol, usually a lowercase letter, that represents one or more numbers
Algebraic expression or variable expression – a mathematical phrase that can include numbers, variables, and operation symbols
Evaluating or Simplifying an expression means substituting numbers for variables and following the order of operations

5. Evaluating Algebraic Expressions
Polynomial – a monomial or sum of monomials
Term – the monomials that makes
up the polynomial
Binomial – 2 unlike terms
Trinomial – 3 unlike terms
Like Term example: 2x and 5x

6. Evaluate a-2b+ab for a=3 and b=-1 Example 1
Substitute 3 for a and -1 for b
Multiply First
To subtract, add the opposite
Add from left to right
Add

7. Try These Problems Evaluate each expression for x = 4 and y = -2
x + y ÷ x
4 + (-2) ÷ 4 = 4 + (-1/2) = 3 ½ = 7/2 = 3.5
3x – 4y + x – y
3(4) – 4(-2) + 4 – (-2) = 12 – (-8) + 4 –(-2) = – (-2) = 24 – (-2) = 26
x + 2x ÷ y – 2y
4 + 2(4) ÷ (-2) – 2(-2) = ÷ (-2) – 2(-2) = 4 + (-4) -2(-2) = 4 + (-4) +4 = 4

8. Evaluate –x2-2(x+1) for x=3 Example 2
-x2 – 2 (x + 1) = -(3)2 – 2 (3 + 1) Substitute 3 for x.
= -9 – 2(4) Simplify the power and the parenthesis.
= -9 – 8 Multiply
= -17 Subtract
Notice the negative

9. Try These Problems Evaluate each expression for c = -3 and d = 5.
c2 – d2
(-3)2 – 52 = 9 – 25 = -16
c(3 - d) – c2
(-3)(3 – 5) – (-3)2 = (-3)(-2) – 9 = 6 – 9 = -3
-d2 – 4(d – 2c)
-(52) – 4(5 – 2(-3)) = -25 – 4(5 +6) = -25 – 4(11) = = -69

10. Real World Connection
ALGEBRA 2 LESSON 1-1
The expression –0.08y 2 + 3y models the percent increase of Hispanic voters in a town from 1990 to In the expression, y represents the number of years since Find the approximate percent of increase of Hispanic voters by 1998.
Since 1998 – 1990 = 8, y = 8 represents the year 1998.
–0.08y2 + 3y = –0.08(8)2 + 3(8)  Substitute 8 for y 19
The number of Hispanic voters had increased by about 19%.

11. Real World Connection Click here to go to page 9 examples on line
ALGEBRA 2 LESSON 1-1
Click here to go to page 9 examples on line