Variables represent unknown numbers and can be combined using the basic operations of addition, subtraction, multiplication, and division. Common algebra variables include x, y, a, and b. The same variable represents the same value, while different variables represent different values. Exponents are used to represent repeated multiplication of a variable by itself. The FOIL method (First, Outside, Inside, Last) is used to expand expressions containing two sets of parentheses.

1. Algebra Review
Variables: letters (sometimes other symbols) are used to
represent unknown numbers, these are called variables.
Common variables: x y a b A B
Same variable = same value
Different variable = different value (but sometimes it is the same!)
ex: x = x , x =/= y , a = a , a =/= A (=/= means does not equal)

2. How to combine variables
addition
x + x = 2x
3a + 5a = 8a
5x + 4y = 5x + 4y
subtraction
x-x=0
3a - 5a = -2a
5x - 4y = 5x - 4y
multiplication
x(x) = x2
3a(5a) = 3(5) (a)(a) = 15a2
5x(4y) = 5(4) (x)(y) = 20xy
division
x/x=1
3a / 5a = (3/5)(a/a) = 3/5
5x / 4y = 5x / 4y

3. Variables with exponents
2 =/= x
x
so they cannot be added
3x2 + 2x = 3x2 + 2x
2 = x(x)
x
so it can be multiplied with x
x2(x) = (x)(x)(x) = x3
x with exponents can also be divided
by x with a different exponent
x5 / x3 = (x)(x)(x)(x)(x) / (x)(x)(x) =
(x)(x) =
2
x

4. F.O.I.L
First Outside Inside Last
(x + 3) (x + 2) =
F = x(x) = x 2
O = x(2) = 2x
I = 3(x) = 3x
L = 3(2) = 6
=x 2 + 2x + 3x + 6
=x 2 +5x +6

5. (a + b + c) (a - b + c)
1. a(a) = a2
2. a(-b) = -ab
3. a (c) = ac
4. b(a) = ab
5. b (-b) = -b 2
6. b(c) = bc
7. c(a) = ac
8. c(-b) = -cb
9. c(c) = c2
2 + -ab + ac + ab + -b2 + bc + ac + -cb + c2
a
2 + 2ac - b2 + c2
=a