Factorize the expression $x^2+xy+xz+yz$.

Given:

The given algebraic expression is $x^2+xy+xz+yz$.

To do:

We have to factorize the expression $x^2+xy+xz+yz$.

Solution:

Factorizing algebraic expressions:

Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution. 

An algebraic expression is factored completely when it is written as a product of prime factors.

Here, we can factorize the expression $x^2+xy+xz+yz$ by grouping similar terms and taking out the common factors. 

The terms in the given expression are $x^2, xy, xz$ and $yz$.

We can group the given terms as $x^2, xy$ and $xz, yz$. 

Therefore, by taking $x$ as common in $x^2, xy$ and $z$ as common in $xz, yz$, we get,

$x^2+xy+xz+yz=x(x+y)+z(x+y)$

Now, taking $(x+y)$ common, we get,

$x^2+xy+xz+yz=(x+y)(x+z)$

Hence, the given expression can be factorized as $(x+y)(x+z)$.