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Chapter 1
Section 2
Algebraic Expressions
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
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
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Substitute 3 for a and
-1 for b
Multiply First
To subtract, add the
opposite
Add from left to right
Add
Try These Problems
Check Understanding p. 12
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
Evaluate –x2-2(x+1) for x=3
Example 2
-x2 – 2 (x + 1) = -32 – 2 (3 + 1) Substitute 3 for x.
= -9 – 2(4)
Simplify the power and
the parenthesis.
= -9 – 8
Multiply
= -17
Subtract
Try These Problems
p. 12 Check Understanding
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
Homework

Textbook page 15 #1-12
Simplifying Algebraic Expressions

Term – a number, a variable, or the product of a
number and one or more variables


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The “parts” of expressions connected with +/Ex:
3x + 5
terms: 3x, 5
6x4 – y
terms: 6x4, y
Coefficient – the numerical factor in a term

Ex: (using the problems above)
3 from 3x
6 from 6x4
-1 from -y
Like Terms
Like terms – have the same variables raised to the
same powers
Ex:

4x2
-ry4
and
and
7x2
65ry4
Non Ex: 7x
and 8x2
t3w and tw3
Combine like terms to simplify expressions

If it helps draw different shapes around like terms
Simplify by Combining Like Terms
Simplify by combining like terms.
2h – 3k + 7(2h – 3k)
2h – 3k + 7(2h – 3k) = 2h – 3k + 14h – 21k
Distributive Property
= 2h + 14h – 3k – 21k
Commutative Property
= (2 + 14)h – (3 + 21)k
Distributive Property
= 16h – 24k
Try These Problems
p. 14 Check Understanding
Simplify by combining like terms
a) 2x2 + 5x – 4x2 + x – x2
a)
-3x2 + 6x
-2(r + s) – (2r + 2s)
b)
a)
-2r + -2s – 2r -2s = -4r -4s
y(1+y) – 3y2 – (y+1)
c)
a)
y + y2 – 3y2 – y – 1 = -2y2 – 1
Finding Perimeter
ALGEBRA 2 LESSON 1-2
Find the perimeter of this figure. Simplify the answer.
c
c
P = c + 2 + d + (d – c) + d + 2 + c + d
c
c
= c + 2+ d + d – c + d + 2 + c + d
c
c
= 2 + 2 + c + 4d
= 2c
+ c + 4d
2
= c + c + 4d
= 2c + 4d
Try These Problems
Check Understanding p. 14
Find the perimeter of each figure.
a)
b)
3c
3x
2c
2x – y
2c
d
2x
y
d
y
3x-y
10x
6c  2 d
3
10c + 2d
d
3c  d
3
Homework

Textbook page 15 problems #21-37