Algebra 2 A
Chapter 1
Section 1
Algebraic Expressions
And Formulas
Algebraic Expressions
ALGEBRA 2 LESSON 1-1
Use the order of operations to simplify each expression.
1. 8 • 3 – 2 • 4
2. 8 – 4 + 6 ÷ 3
3. 24 ÷ 12 • 4 ÷ 3
4. 3 • 82 + 12 ÷ 4
5. 27 + 18 ÷ 9 – 32 + 1
6. (40 + 24) ÷ 8 – (23 + 1)
Algebraic Expressions
ALGEBRA 2 LESSON 1-1
Solutions
1. 8 • 3 – 2 • 4 = (8 • 3) – (2 • 4) = 24 – 8 = 16
2. 8 – 4 + 6 ÷ 3 = 8 – 4 + (6 ÷ 3) = 8 – 4 + 2 = (8 – 4) + 2 = 4 + 2 = 6
3. 24 ÷ 12 • 4 ÷ 3 = (24 ÷ 12) • 4 ÷ 3 = 2 • 4 ÷ 3 = (2 • 4) ÷ 3 = 8 ÷ 3 =
8 or 2 2
3
3
4. 3 • 82 + 12 ÷ 4 = 3 • 64 + 12 ÷ 4 + (3 • 64) + (12 ÷ 4) = 192 + 3 = 195
5. 27 + 18 ÷ 9 – 32 + 1 = 27 + 18 ÷ 9 – 9 + 1 = 27 + (18 ÷ 9) – 9 + 1 =
27 + 2 – 9 + 1 = (27 + 2) – 9 + 1 = 29 – 9 + 1 = (29 – 9) + 1 = 20 + 1 = 21
6. (40 + 24) ÷ 8 – (23 + 1) = (40 + 24) ÷ 8 – (8 + 1) = 64 ÷ 8 – 9 =
(64 ÷ 8) – 9 = 8 – 9 = –1
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
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

Evaluate a-2b+ab for a=3 and b=-1
Example 1
a  2b  ab  3  2(1)  3(1)
 3  (2)  (3)
 3  2  ( 3)
 5  ( 3)
 2





Substitute 3 for a and
-1 for b
Multiply First
To subtract, add the
opposite
Add from left to right
Add
Try These Problems
Evaluate each expression for x = 4 and y = -2
a) x + y ÷ x
a)
4 + (-2) ÷ 4 = 4 + (-1/2) = 3 ½ = 7/2 = 3.5
3x – 4y + x – y
b)
a)
3(4) – 4(-2) + 4 – (-2) = 12 – (-8) + 4 –(-2)
= 20 + 4 – (-2) = 24 – (-2) = 26
x + 2x ÷ y – 2y
c)
a)
4 + 2(4) ÷ (-2) – 2(-2) = 4 + 8 ÷ (-2) – 2(-2)
= 4 + (-4) -2(-2) = 4 + (-4) +4 = 4
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
Try These Problems
Evaluate each expression for c = -3 and d = 5.
a) c2 – d2
a)
(-3)2 – 52 = 9 – 25 = -16
c(3 - d) – c2
b)
a)
(-3)(3 – 5) – (-3)2 = (-3)(-2) – 9 = 6 – 9 = -3
-d2 – 4(d – 2c)
c)
a)
-(52) – 4(5 – 2(-3)) = -25 – 4(5 +6) = -25 – 4(11)
= -25 -44 = -69
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 2000. In the expression, y represents the number of years since
1990. 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%.
Real World Connection
ALGEBRA 2 LESSON 1-1
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