MATHEMATICS

ALGEBRA

Expanding
a(b+c) = ab+ac
(a+b)² = a²+2ab+b²
(a-b)² = a²-2ab+b²
(a+b)(a+c) = a²+ac+ab+bc
(a+b)(c+d)=ac+ad+bc+bd
(a+b)³ = a³+3a²b+3ab²+b³
(a-b)³ = a³-3a²b+3ab²-b³
a²-b² = (a+b)(a-b)
a³+b³ = (a+b)(a²-ab+b²)
a³b-ab = ab(a+1)(a-1)
a²-2ab+b² = (a-b)²
a³-b³ = (a-b)(a²+ab+b²)

Laws of Exponents
a^ra^s = a^r+s
^{a^r}/_a^s = a^r-s
^{a^ra^s}/_a^p = a^r+s-p
(a^r)^s = a^rs
(ab)^r = a^rb^r
(a/b)^r = ^{a^r}/_b^r (b¹0)
a⁰ = 1 (a¹0)
a^-r = ¹/_a^r (a¹0)

if r and s are positive integers

Logarithms
Log(xy) = Log x + Log y
Log x^r = r Log x
Log x = n « x = 10ⁿ (Common log)
Log_ax = n « x = aⁿ (Log to the base a)
Ln x = n « x = eⁿ (Natural log)
Log(^x/_y) = Log x-Log y

e=2.71828183

Quadratic Formula

When given a formula in the form of a quadratic equation ® ax²+bx+c=0

The solution can be derived using the quadratic formula ®
x = -b±Ö(b²-4ac)

2a