Question

factor.
$x^2 - 4x + 4$

Explanation:

Step1: Identify the form of the quadratic

The quadratic \(x^2 - 4x + 4\) is a perfect square trinomial. The general form of a perfect square trinomial is \(a^2 - 2ab + b^2=(a - b)^2\).

Step2: Match the terms

Here, \(a = x\) (since \(x^2=a^2\)) and \(2ab = 4x\). Substituting \(a = x\) into \(2ab = 4x\), we get \(2\times x\times b=4x\), which simplifies to \(2b = 4\), so \(b = 2\) (and \(b^2 = 4\), which matches the constant term).

Step3: Apply the formula

Using the formula \(a^2 - 2ab + b^2=(a - b)^2\) with \(a = x\) and \(b = 2\), we have \(x^2 - 4x + 4=(x - 2)^2\).

Answer:

\((x - 2)^2\)