91Ó°ÊÓ

Find the factorization of $2x^2$ and $3xz$.

$$\begin{gathered} 2x^2=2â‹\dots xâ‹\dots x \\ 3xz=3â‹\dots xâ‹\dots z \end{gathered}$$

From the factorization of $2x^2$and $3xz$, it can be noticed that the greatest common factor of $2x^2$and $3xz$is $x$.

Therefore, the greatest common factor of $2x^2$and $3xz$is $x$.

Find the factorization of $2xy$ and $3yz$.

$$\begin{gathered} 2xy=2â‹\dots xâ‹\dots y \\ 3yz=3â‹\dots yâ‹\dots z \end{gathered}$$

From the factorization of $2xy$and $3yz$, it can be noticed that the greatest common factor of $2xy$and $3yz$is $y$.

Therefore, the greatest common factor of $2xy$and $3yz$is $y$.

Therefore, it is obtained that:

$2x^2−3xz−2xy+3yz=x\left(2x\right)−x\left(3z\right)−y\left(2x\right)+y\left(3z\right)$

The distributive property states that:

$ab+ac=a\left(b+c\right)$

Now, use the distributive property to factor out the greatest common factor.

Therefore, it is obtained that:

role="math" localid="1647949844013" $$\begin{gathered} 2x^2−3xz−2xy+3yz=x\left(2x\right)−x\left(3z\right)−y\left(2x\right)+y\left(3z\right) \\ =x\left(2x−3z\right)−y\left(2x−3z\right) \\ =\left(2x−3z\right)\left(x−y\right)\left(\text{takeout}2x−3z\text{ascommonfactor}\right) \end{gathered}$$

Therefore, the factorization of the given polynomial is $\left(2x−3z\right)\left(x−y\right)$.