Question

what is the factored form of $x^2 - 4x + 4$
$square$ $(x - 2)^2$
$square$ $(x + 2)^2$
$(x - 4)^2$
$(x + 4)^2$
rewatch

Explanation:

Step1: Recall the perfect square formula

The perfect square trinomial formula is \(a^2 - 2ab + b^2=(a - b)^2\).

Step2: Identify \(a\) and \(b\) in the given expression

For the expression \(x^2-4x + 4\), we can see that \(a=x\) (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 \(b = 2\). Also, \(b^2=4\) (since the constant term is 4).

Step3: Apply the perfect square 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:

\((x - 2)^2\) (corresponding to the first option: \((x - 2)^2\))