Algebraic Expressions [WIP]

When multiplying two expressions

1.

(a+b)2=a2+2ab+b2(a+b)^2 = a^2 + 2ab + b^2

2.

(ab)2=a22ab+b2(a-b)^2 = a^2-2ab+b^2

3.

(a+b)(ab)=a2b2(a+b)(a-b)=a^2-b^2

4.

(x+a)(x+b)=x2+(a+b)x+ab(x+a)(x+b)=x^2+(a+b)x+ab

5.

(x+y+z)2=x2+y2+z2+2xy+2xz+2yz(x+y+z)^2 = x^2 + y^2 + z^2 + 2xy + 2xz + 2yz

When multiplying three expressions

1.

(x+y)3=x3+y3+3xy(x+y)(x+y)^3=x^3+y^3+3xy(x+y)

2.

(xy)3=x3y33xy(xy)(x-y)^3 = x^3-y^3-3xy(x-y)

3.

x3+y3+z33xyz=(x+y+z)(x2+y2+z2xyyzzx)x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)