Question

Factorize x^2y^2+xyz+xy+z​

Answer 1

Given:

$\sf \bullet \: \: x^{2}y^{2} + xyz + xy + z$

To do:

Factorize

Solution:

$\sf : \: \implies x^{2}y^{2} + xyz + xy + z$

~Do grouping

$\sf : \: \implies x^{2}y^{2} + xyz + xy + z$

$\sf : \: \implies ( x^{2}y^{2} + xyz ) + ( xy + z )$

~Factor out xy

$\sf : \: \implies xy( xy + z ) + ( xy + z )$

$\sf : \: \implies xy( xy + z ) + 1( xy + z )$

$\boxed{\bf{ ( xy + 1 ) ( xy + z )}} \: \: \bigstar$

______________

• Henceforth, the factorized form is ( xy + 1 )( xy + z )

Answer 2

Given,

$x^2y^2+xyz+xy+z$

• We can find the factors of given equation by using factorization splitting method.

First take common terms

$xy(1+xy)+z(1+xy)$

It can also written as

$(1+xy)(xy+z)$

Therefore, the factors of $x^2y^2+xyz+xy+z$ is $(1+xy)(xy+z)$.