Algebra

Basics

a+b = b+a

a*b = b*a

(a+b)+c = a+(b+c)

(a*b)*c = a*(b*c)

a*(b+c)=a*b + a*c

Factorial:

n! = n*(n-1)*(n-2)*...*1

alternative: n! = 1*2*3*...*n

example: 4! = 4*3*2*1 = 24

Laws of Exponents

(a^m) (aⁿ) = a^m+n

(ab)^m = a^mb^m

(a^m)ⁿ = a^mn

a⁰ = 1

(a^m)/(aⁿ) = a^m-n

a^-m = 1/(a^m)

Note:

(-1) ⁿ = 1 is true if

n is an even integer ( n modulo 2 = 0)

(-1) ⁿ = -1 is true if

n is an odd integer ( n modulo 2 ≠ 0)

Quadratic Formula

An equation that has the form: ax²+bx+c = 0 can be solved via this formula:

Binomal Theorem

(a + b)¹ = a + b

(a + b)² = a² + 2ab + b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

Difference of Squares

a² - b² = (a - b) (a + b)

Difference of Cubes

a³ - b³ = (a - b)(a² + ab + b²)

Rules of Zero

0/x = 0 where x is not equal to 0.

a⁰ = 1 & 0⁰ = 1

0^a = 0 where a is not equal to zero

a*0 = 0

a/0 is undefined (don't do it, you will open a black hole!)