Question

In the following exercises, factor each expression using any method$u^2-12u+36$

Short answer

The factors are$\left(u-6\right)\left(u-6\right)$

Step-by-step solution

Step 1. Given Information

The trinomial is $u^2-12u+36$

Find the factors.

Step 2. Factor the trinomial

Split the middle term of trinomial to find factors

$$\begin{gathered} u^2-12u+36 \\ {u}^2-6u-6u+36 \end{gathered}$$

Factor it

$$\begin{gathered} u\left(u-6\right)-6\left(u-6\right) \\ \left(u-6\right)\left(u-6\right) \end{gathered}$$

Step 3. Check

Multiply the factors.

$$\begin{gathered} \left(u-6\right)\left(u-6\right) \\ {u}^2-6u-6u+36 \\ {u}^2-12u+36 \end{gathered}$$