Corollary : Lopanasthapanabhyam

It is very difficult to factorise the long quadratic (2x² + 6y² + 3z² + 7xy + 11yz + 7zx)

But "Lopana-Sthapana" removes the difficulty. Eliminate z by putting z = 0.

Hence the given expression E = 2x² + 6y² + 7xy = (x+2y) (2x+3y)

Similarly, if y=0, then E = 2x² + 3z² + 7zx = (x+3z) (2x+z)

Hence E = (x+2y+3z) (2x+3y+z)

Factorise 2x2 + 2y2 + 5xy + 2x- 5y –12 = (x+3) (2x-4) and (2y+3) (y-4)

Hence, E = (x+2y+3) (2x+y-4)