Q. 244 - Intermediate Algebra

Question

In the following exercises, factor completely.  

$64x^2+16xy+y^2$

Step-by-Step Solution

Answer

The required factors are  ${(8x+y)}^2$

Step 1. Given Information

The given expression is $64x^2+16xy+y^2$

Step 2. Calculation

We will find the factors by using the perfect square trinomial pattern.

$$\begin{gathered} 64x^2+16xy+y^2={\left(8x\right)}^2+2\times 8x\times y+{\left(y\right)}^2 \\ ={(8x+y)}^2 \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} {(8x+y)}^2={\left(8x\right)}^2+2\times 8x\times y+{\left(y\right)}^2 \\ =64x^2+16xy+y^2 \end{gathered}$$