Question

Factorize the following:
$x^{2}yz+x{y}^{2}z+xy{z}^2$

Answer 1

Terms of the given expression $x^{2}yz+x{y}^{2}z+xy{z}^2$ are $x^{2}yz,x{y}^{2}z\text{and}xy{z}^2$

$x^{2}yz=x\times x\times y\times z$
$x{y}^{2}z=x\times y\times y\times z$
$xy{z}^2=x\times y\times z\times z$

Greatest common factors $=x\times y\times z=xyz$
$\therefore x^{2}yz+x{y}^{2}z+xy{z}^2$
$=xyz(x+y+z)$

Hence, the factorized form is $xyz(x+y+z)$