Question

Factor by Grouping
In the following exercises, factor by grouping.

$mn-6m-4n+24$.

Short answer

The obtained factors by using the grouping method for the given expression$mn-6m-4n+24$ are,$\left(n-6\right)\left(m-4\right)$.

Step-by-step solution

Given expression is,

$mn-6m-4n+24$.

The objective is, we need to find the factors for the given expression by using the grouping method.

First group the terms with the common factors.

$mn-6m-4n+24=\left(mn-6m\right)+\left(-4n+24\right)$

Now factor out the common terms from each group.

$$\begin{gathered} mn-6m-4n+24=m\left(n-6\right)-4\left(n-6\right) \\ =\left(n-6\right)\left(m-4\right) \end{gathered}$$

The obtained factors for the given expression is,$\left(n-6\right)\left(m-4\right)$.

Step 3 let us check  the answer by multiplying the factors.

$$\begin{gathered} \left(n-6\right)\left(m-4\right)=nm-4n-6m+24 \\ =mn-6m-4n+24 \end{gathered}$$

which is true.