Basic Identities

(x+y)² =x²+2xy+y²
(x-y)² =x²-2xy+y²
(x+a)×(x+b) = x²+(a+b)x+ab
(x-a)×(x-b) = x²-(a+b)x +ab
x²-y² = (x+y)×(x-y)
x²+y²= (x+y)²-2xy = (x-y)²+2xy
(x+y)³ = x³+3x²y+3xy²+y³
(x+y)³ = x³-3x²y+3xy²+y³
x³+y³ =(x+y)(x²-xy+y²)
x³-y³ = (x-y)(x²+xy+y²)
(x+y+z)² = x²+y²+z²+2xy+2yz+2zx
x³+y³+z³-3xyz = (x+y+z)(x²+y²+z²-xy-yz-zx)
x³+y³+z³-3xyz = ½(x+y+z)[(x-y)²+(y-z)²+(z-x)²]
Roots of quadratic equation ax²+bx+c=0
x=[-b±√(b²-4ac)]÷2a