Algebra

Factoring Formulas:

$$a^2 - b^2 = (a-b)(a+b)$$

$$a^3 - b^3 = (a-b)(a^2+ab+b^2)$$

$$a^3 + b^3 = (a+b)(a^2-ab+b^2)$$

If n is odd then (a + b) is a factor of $a^n + b^n$.

If n is even then (a - b) is a factor of $a^n - b^n$.

Product Formulas:

$$(a-b)^2 = a^2 - 2ab +b^2$$

$$(a+b)^2 = a^2+ 2ab +b^2$$

$$(a-b)^3 = a^3 - 3a^2b+3ab^2 -b^3$$

$$(a+b)^3 = a^3 + 3a^2b+3ab^2 +b^3$$

$$(a+b+c)^2 = a^2 + b^2 +c^2+2ab+2bc+2ca$$

Logarithms: 

$$y = \log_a x \Leftrightarrow x = a^y , \; a>0, a \neq  1$$

$$\log_a 1 = 0$$

$$\log_a a =1$$

$$\log_a (xy) = \log_a x + \log_a y$$

$$\log_a \frac{x}{y} = \log_a x - \log_a y$$

$$\log_a x^n = n \log_a x$$

$$\log_a x = \frac{ \log_c x}{ \log_c a} = \log_c x.\log_a c$$

$$a^{ \log_a x} = x$$

Compound Interest Formulas:

A : Future value

P: Initial investment

r : Annual interest rate

t : Number of years invested

n : Number of times compounded per year

$$A = P \left ( 1 + \frac{r}{n} \right )^{nt}$$

Continuous compound interest then,

$$A = P e^{rt}$$

Simple interest then,

$$A = P(1+rt)$$