Question

question
factor.
$x^2 - 16x + 64$
answer attempt 1 out of 2

Explanation:

Step1: Recall perfect square formula

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

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

For \(x^2-16x + 64\), we have \(a = x\) (since \(x^2=a^2\)), and \(2ab=16x\). Substituting \(a = x\) into \(2ab = 16x\), we get \(2\times x\times b=16x\), which simplifies to \(b = 8\) (dividing both sides by \(2x\)). Also, \(b^2=8^2 = 64\), which matches the constant term.

Step3: Apply the formula

Using the perfect square trinomial formula \(a^2-2ab + b^2=(a - b)^2\) with \(a=x\) and \(b = 8\), we get \(x^2-16x + 64=(x - 8)^2\).

Answer:

\((x - 8)^2\)