Q. 137. - Intermediate Algebra

Question

In the following exercises, factor each expression using any method $r^2-20rs+64s^2$

Step-by-Step Solution

Answer

The factors are $\left(r-16s\right)\left(r+4s\right)$

Step 1. Given Information

The trinomial is$r^2-20rs+64s^2$

Find factors by splitting middle term  

Step 2. Factor the trinomial

Split the middle term of trinomial to find factors

Find two numbers such as their product is 64 and sum is $-20$

The numbers are  $-16$and $-4$

$r^2-20rs+64s^2$

$r^2-16rs-4rs+64s^2$

Factor it

$$\begin{gathered} r\left(r-16s\right)-4s\left(r-16s\right) \\ \left(r-16s\right)\left(r-4s\right) \end{gathered}$$

Step 3. Check

Multiply the factor

$$\begin{gathered} \left(r-16s\right)\left(r-4s\right) \\ {r}^2-16rs-4rs+64s^2 \\ {r}^2-20rs+64s^2 \end{gathered}$$