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- (x+y)(x+y) = x²+2xy+y²
- (x-y)(x-y) = x²-2xy+y²
- (x+y)(x-y) = x²-y²
- (x+a)(x+b) = x²+(a+b)x+ab
- (x+y+z)² = x²+y²+z²+2xy+2xz+2yz
- (x+y)³ = x³+y³+3x²y+3y²x or x³+y³+3xy(x+y)
- (x-y)³ = x³-y³-3x²y+3y²x or x³-y³-3xy(x-y)
- x³+y³+z³-3xyz = (x+y+Z)(x²+y²+z²-xy-xz-yz)
- x³+y³ = (x+y)(x²-xy+y²)
- x³-y³ = (x-y)(x²+xy+y²)
- if x+y+z = 0 then x³+y³+z³ = 3xyz