Evaluating Expressions


If you need to evaluate an expression, just replace the variable
(the letter) with the number given.


Here are some examples:
1) Evaluate: 3A + 3B

if A=2 and B=6
Plug the value 2 for every letter A and

the value 6 for the letter B


3(2) +3(6) =
6 + 18=
24


2) Evaluate: 2y-5t-7v

if y=1, t=6, v=-1
Plug the value 1 for every letter y, the value 6 for the letter t,

and -1 for the letter v.


2(1)-5(6)-7(-1)=
2-30+7=
-21
3) Evaluate:

  
if a=-1
Plug the value of –1 into every letter a:



3(1)+2+6=
3+2+6=
11







 

Let's Practice

Let's Practice

Let's Practice

Let's Practice

Let's Practice


When simplifying expressions, you need to group all the like terms together.

For example:
Simplify the following expression: 3X+ 2Y-4X+6Y
Group together the terms that are alike: 3X-4X + 2Y+6Y= -X+ 8Y


Let’s do another example:
2(x-2y)-(x+3y)
Let’s do the parenthesis first, by distributing the 2 and the negative (-)

in front of the parenthesis
2x-4y-x-3y
Now, just group the like terms:
2x-x-4y-3y
2x-7y


Another example:
-3a(4+b)-4b(3-a)
Let’s distribute the numbers in front of the parenthesis:
-12a-3ab-12b+4ab
Now you can group the like terms:

 -12a-12b+ab



Simplifying Expressions

Translating  Expressions

Expressions can be translated from English to a math expression or vice versa.
There are key words to use when you are translating an expression.




Exponential  Expressions


Let’s learn the rules to treat exponents with examples:


Rule 1: When you multiply exponents with the same base, you need to keep the base and add the exponents on the top:

Examples






Rule 2: When you have a negative exponent, you can change it

to positive by finding its inverse: 

Examples







Rule 3: When you are raising a power to a power, you need to multiply:

Examples






Rule 2: When you divide exponents with the same base, you will subtract them

Example






Rule 5: When you raise an exponent to ZERO, the answer is 1.



**Be Careful, if you have a negative in front, then the answer is -1.



BUT, if you have it with a parenthesis like this, then the answer is 1



Rule 6: When you raise an exponent to 1, the answer is the same exponent.









x
3


x
6

=

x

9






(
3
a
)

4

=

3
4


a
4

=
81

a
4


When you multiply polynomials, you need to follow the rules of exponents.
Let’s do an example:



Distribute the variables xy to every single term:



Let’s do another example:
Simplify

(3x-y)(x+2y)


STEP ONE: Multiply the 3x by every single term on the second parenthesis
and the same with -y

STEP TWO: Just group the terms



Another example:

(a-b)(a+b)





Multiplying Expressions



2
3


2
2

=

2
5



a
5


a
6

=

a

11




3


(
-
1
)

2

-
2

(
-
1
)

+
6
=




3

-
2


=

1

3
2






1

X

-
3



=

X
3





2
3

=
8






a
5


b
7


c
10




a
8


b
3


c
2







a

5
-
8



b

7
-
3



c

10
-
2


=

a

-
3



b
4


c
8

=



b
4


c
8




a
3







X
0

=
1



-

X
0

=
-
1





(
-
X
)

0

=
1





(
a
)

1

=
a



x
y

(
3
x
-

y
2

)





(
3
×
y
-

y
2

y
)

=
3

x
2

y
-

y
3




3

x
2

+
6
x
y
-
x
y
-

y
2

=
3

x
2

+
5
x
y
-

y
2





a
2

+
a
b
-
a
b
-

b
2

=

a
2

+
0
-

b
2

=

a
2

-

b
2


Factoring: 

Factoring by Greatest Common Factor 


Let’s do an example:

Factor the following expression by the GCF



The Greatest Common Factor is    , the case is the letter with the lowest exponent then you can factor out    and you have : 



                                       Let’s do another example:


The GCF is 2xy, that is the most you can extract from the binomial 

                                                2xy(2x-1)

                                            Last example


Here the GCF is only 2, there there is GCF for the letters: 





a
6

+

a
4




a
4



a
4



a
4

(

a
2

+
1
)

4

x
2

y

2
x
y

6

a
2

b

2
a
b
+
12

2
(
3

a
2

b

a
b
+
6
)

Factoring by Grouping


When you factor by grouping you will have four terms

Let's do an example: 



The first step is to make an invisible line between the four factors and find the GCF for              and (5x+20)

The GFC               for is X

The GCF for 5x+20 is 4

Now we can factor the X for the first term: 


Also factor the second term 5x+20 

5x+ 20 = 5(x+4)

Finally 





Let's Practice



X
2

+
4
x
+
5
x
+
20

Let's Practice



x
2

+
4
x


x
2

+
4
x


x
2

+
4
x
=
x
(
x
+
4
)


x
2

+
4
x
+
5
x
+
20
=
x
(
x
+
4
)
+
5
(
x
+
4
)
=
(
x
+
4
)
(
x
+
5
)

Factoring Trinomials

Difference of Squares

Sum and Differences of Cubes

Rational Expressions

System of Equations

Graphing Inequalities 

Equations

Inequalities

Coordinate Geometry

Radical Expressions

Quadratic Equations

Complex Numbers

Functions 

Graphing the Quadratic Functions

Advance Topics

Sequences

Series

Trigonometry