91Ó°ÊÓ

Find the factorization of $a^2$and $4ac$.

$$\begin{gathered} a^2=aâ‹\dots a \\ 4ac=2â‹\dots 2â‹\dots aâ‹\dots c \end{gathered}$$

From the factorization of $a^2$and $4ac$, it can be noticed that the greatest common factor of $a^2$and $4ac$is $a$.

Therefore, the greatest common factor of $a^2$and $4ac$is $a$.

Find the factorization of $ab$ and $4bc$.

$$\begin{gathered} ab=aâ‹\dots b \\ 4bc=2â‹\dots 2â‹\dots bâ‹\dots c \end{gathered}$$

From the factorization of $ab$and $4bc$, it can be noticed that the greatest common factor of $ab$and $4bc$is $b$.

Therefore, the greatest common factor of $ab$and $4bc$is $b$.

Therefore, it is obtained that:

$a^2−4ac+ab−4bc=a\left(a\right)−a\left(4c\right)+b\left(a\right)−b\left(4c\right)$

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="1647949311355" $$\begin{gathered} a^2−4ac+ab−4bc=a\left(a\right)−a\left(4c\right)+b\left(a\right)−b\left(4c\right) \\ =a\left(a−4c\right)+b\left(a−4c\right) \\ =\left(a−4c\right)\left(a+b\right)\left(\text{takeout}a−4c\text{ascommonfactor}\right) \end{gathered}$$

Therefore, the factorization of the given polynomial is $\left(a−4c\right)\left(a+b\right)$.