#### 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

#### 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:

#### 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.

${x}^{3}{x}^{6}={x}^{9}$
${\left(3a\right)}^{4}={3}^{4}{a}^{4}=81{a}^{4}$

#### Multiplying Expressions

${2}^{3}{2}^{2}={2}^{5}$
${a}^{5}{a}^{6}={a}^{11}$
$3{\left(-1\right)}^{2}-2\left(-1\right)+6=$
${3}^{-2}=\frac{1}{{3}^{2}}$
$\frac{1}{{X}^{-3}}={X}^{3}$
${2}^{3}=8$
$\frac{{a}^{5}{b}^{7}{c}^{10}}{{a}^{8}{b}^{3}{c}^{2}}$
${a}^{5-8}{b}^{7-3}{c}^{10-2}={a}^{-3}{b}^{4}{c}^{8}=\frac{{b}^{4}{c}^{8}}{{a}^{3}}$
${X}^{0}=1$
$-{X}^{0}=-1$
${\left(-X\right)}^{0}=1$
${\left(a\right)}^{1}=a$
$xy\left(3x-{y}^{2}\right)$
$\left(3×y-{y}^{2}y\right)=3{x}^{2}y-{y}^{3}$
$3{x}^{2}+6xy-xy-{y}^{2}=3{x}^{2}+5xy-{y}^{2}$
${a}^{2}+ab-ab-{b}^{2}={a}^{2}+0-{b}^{2}={a}^{2}-{b}^{2}$

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

${a}^{6}+{a}^{4}$
${a}^{4}$
${a}^{4}$
${a}^{4}\left({a}^{2}+1\right)$
$4{x}^{2}y-2xy$
$6{a}^{2}b-2ab+12$
$2\left(3{a}^{2}b-ab+6\right)$

#### 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

${X}^{2}+4x+5x+20$

#### Let's Practice

${x}^{2}+4x$
${x}^{2}+4x$
${x}^{2}+4x=x\left(x+4\right)$
${x}^{2}+4x+5x+20=x\left(x+4\right)+5\left(x+4\right)=\left(x+4\right)\left(x+5\right)$