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=

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.


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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:
Let’s do the parenthesis first, by distributing the 2 and the negative (-)

in front of the parenthesis
Now, just group the like terms:

Another example:
Let’s distribute the numbers in front of the parenthesis:
Now you can group the like terms:


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:


Rule 2:

When you have a negative exponent, you can change it

to positive by finding its inverse: 


Rule 3:

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


Rule 4:

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


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:


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:


Multiplying Expressions


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 



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: 



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