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

(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca

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

(ax+b)(cx+d)=acx^2+(ad+bc)x+bd

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

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