I will keep adding formulas to this formula sheet. You are welcome to add more onto these.

Algebra

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

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

(a+b)^3 = a^3 + b^3 + 3ab*(a+b)

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

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

Notes:

(a+b) is always a factor of [a^n + b^n] IFF n is positive odd integer

(a-b) is always a factor [a^n - b^n] IFF n is a positive integer

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