(a+b)² = a²+2ab+b²

a²-b² = (a+b)(a-b)

(a-b)³ = a³-3a²b+3ab²-b³

if: x^a=x^b, then: a=b (except if: x=1)

x^-a = 1/x^a   AND  1/x^-a = x^a

(x^a)(x^b) = x^a+b

(x^a)^b = x^ab

x^a/x^b = x^a-b = 1/x^b-a

x⁰ = 1

(x^a)(y^a) = (xy)^a

(x/y)^a = x^a/y^a

(x+a)(x+b) = x²+ax+bx+ab = x²+(a+b)x+ab