Question

factor.
$81w^2 - 36w + 4$

Explanation:

Step1: Identify the form

The quadratic \(81w^2 - 36w + 4\) looks like a perfect square trinomial. The form of a perfect square trinomial is \(a^2 - 2ab + b^2=(a - b)^2\).

Step2: Find \(a\) and \(b\)

For \(81w^2=(9w)^2\), so \(a = 9w\). For the constant term, \(4 = 2^2\), so \(b = 2\). Now check the middle term: \(2ab=2\times9w\times2 = 36w\), which matches the middle term (with a negative sign, so it's \(-2ab\)).

Step3: Apply the formula

Using \(a^2 - 2ab + b^2=(a - b)^2\), substitute \(a = 9w\) and \(b = 2\). So \(81w^2 - 36w + 4=(9w - 2)^2\).

Answer:

\((9w - 2)^2\)