Vanessa Graulich

Certified Math Teacher

6th-12th

#### 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

#### 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:

#### 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,

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

#### 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)