Q 47E - Intermediate Algebra

Question

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

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

Step-by-Step Solution

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 1 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.

Step 2 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.