Question

Factorize 27x^2+y^2+125z^2-45xyz

Answer 1

Answer:

I really suspect you meant to write:

                  Factorize 27x³ + y³ + 125z³ - 45xyz.

Proceeding with that assumption...

Use

   a³ + b³ + c³ - 3abc  =  (a + b + c)(a² + b² + c² - ab - bc - ca)

Then

   27x³ + y³ + 125z³ - 45xyz

=  (3x)³ + y³ + (5z)³ - 3(3x)y(5z)

=  (3x + y + 5z)((3x)² + y² + (5z)² - (3x)y - y(5z) - (5z)(3x))

=  (3x + y + 5z)(9x² + y² + 25z² - 3xy - 5yz - 15zx)