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






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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 4:

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

Examples






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










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

Factoring: 

Factoring by Greatest Common Factor 


Let’s do an example:

Factor the following expression by the GCF



The Greatest Common Factor 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)

   


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

5x+20=5(x+4)

Now we can factor the X for the first term: 




Finally 

(X+5)(X+4)





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