Algebra Formulae

Algebra
Factors and expansions a, b real; n positive integer
(a ± b)² = a² ± 2ab + b²
(a ± b)³ = a³ ± 3a²b + 3ab² ± b³
(a ± b)4 = a4 ± 4a³b + 6a²b² ± 4ab³ + b4
a² - b² = (a - b)(a + b)
a² + b² = (a - bi)(a + bi)
a³ - b³ = (a - b)(a² + ab + b²)
a³ + b³ = (a + b)(a² - ab + b²)
a4 + b4 = (a² + 2½ab + b²)(a² - 2½ab + b²)
an - bn = (a - b)(an-1 + an-2b + ... + bn-1), for n even
an + bn = (a + b)(an-1 - an-2b - ... - bn-1), for n odd

Powers and roots a > 0, b > 0, x, y real
axay = ax+y
ax / ay = ax-y
axbx = (ab)x
ax / bx = (a / b)x
a-x = 1 / ax

Proportion
If a / b = c / d, then (a ± b) / b = (c ± d) / d, and (a - b) / (a + b) = (c - d) / (c + d)

Common Irrational Numbers (includes the first 12 prime numbers)
To find the root of a number which is not prime – do a prime factorization of the number and multiply / exponentiate appropriately.