Question

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

$64z^2-16z+1$

Short answer

The factor of the trinomial is${\left(8x-1\right)}^2$.

Step-by-step solution

Step 1. Given information.

Consider the given trinomial.

$64z^2-16z+1$

Step 2. Formula used 

The general formula for pefect square trinomial is

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

Step 3. Find the factor of perfect square trinomial.

The middle term of the trinomial is negative, so the binomial square will be ${\left(a-b\right)}^2$.

${\left(8x\right)}^2-2·8x·1+{\left(1\right)}^2$

Write factor.

${\left(8x-1\right)}^2$