Learn Basic Formulas of Algebra for Math Preparation

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