#### 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

#### Let's Practice

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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)

#### Let's Practice

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