Q. 242 - Intermediate Algebra

Question

In the following exercises, factor completely.  

$49b^2-112b+64$

Step-by-Step Solution

Answer

The required factors are ${(7b-8)}^2$

Step 1. Given Information

The given expression is $49b^2-112b+64$

Step 2. Calculation

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

$$\begin{gathered} 49b^2-112b+64={\left(7b\right)}^2-2\times 7b\times 8+8^2 \\ ={(7b-8)}^2 \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} {(7b-8)}^2={\left(7b\right)}^2-2\times 7b\times 8+8^2 \\ =49b^2-112b+64 \end{gathered}$$