Q. 249 - Intermediate Algebra

Question

In the following exercises, factor completely.  

$k^4-16$

Step-by-Step Solution

Answer

The required factors are $(k^2+4)(k-2)(k+2)$

Step 1. Given Information

The given expression is $k^4-16$

Step 2. Calculation

We will find the factors by using difference of square patterns,

$$\begin{gathered} k^4-16={\left(k^2\right)}^2-4^2 \\ =(k^2-4)(k^2+4) \\ =(k^2+4)(k^2-2^2) \\ =(k^2+4)(k-2)(k+2) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} (k^2+4)(k-2)(k+2)=(k^2+4)(k^2-2^2) \\ =(k^2-4)(k^2+4) \\ ={\left(k^2\right)}^2-4^2 \\ =k^4-16 \end{gathered}$$