Question

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

Short answer

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

Step-by-step solution

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

localid="1645525209432" $$\begin{gathered} r\left(r-16s\right)-4s\left(r-16s\right) \\ \left(r-16s\right)\left(r-4s\right) \end{gathered}$$

Step 3. Check

Multiply the factor

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