Question

Factorise: 125x^3 - 27y^3 + z^3 + 45xyz

Answer 1

Hope it can help u ...

Answer 2

Answer: $(5x-3y+z)(25x^2+9y^2+z^2+15xy+3yz-5xz)$

Step-by-step explanation:

Required Identity :

$x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-xz)$    (1)

$25x^3 - 27y^3 + z^3 + 45xyz$ can be written as :

$(5x)^3+(-3y)^3+z^3-3(5x)(-3y)(z)\\\\=(5x-3y+z)((5x)^2+(-3y)^2+z^2-5x(-3y)-(-3y)z-5xz)\\\\=(5x-3y+z)(25x^2+9y^2+z^2+15xy+3yz-5xz)$

The factorization of $25x^3 - 27y^3 + z^3 + 45xyz$ is

$(5x-3y+z)(25x^2+9y^2+z^2+15xy+3yz-5xz)$