Question

In the following exercises, factor completely using the perfect square trinomials pattern.

$100x^2-20x+1$

Short answer

The complete factor of the polynomial is${\left(10x-1\right)}^2$

Step-by-step solution

Step 1. Given information.

Consider the given polynomial.

$100x^2-20x+1$

Step 2. Formula used

The general formula for pefect square trinomial is

$a^2-2ab+b^2={\left(a-b\right)}^2$

Step 3. Using the perfect square trinomial to find the complete factor.

$$\begin{gathered} {\left(10x\right)}^2-2·10x·1+{\left(1\right)}^2 \\ {\left(10x-1\right)}^2 \end{gathered}$$