Question

factor.
$x^2 - 16xu + 64u^2$

Explanation:

Step1: Identify the form of the quadratic

The given expression \(x^2 - 16xu + 64u^2\) is a quadratic trinomial in the form \(a^2-2ab + b^2\), where \(a=x\) and we need to find \(b\) such that \(2ab = 16xu\).

Step2: Find the value of \(b\)

Substituting \(a = x\) into \(2ab=16xu\), we get \(2\times x\times b=16xu\). Dividing both sides by \(2x\) (assuming \(x
eq0\)), we have \(b = \frac{16xu}{2x}=8u\). Also, \(b^2=(8u)^2 = 64u^2\), which matches the constant term of the trinomial.

Step3: Apply the perfect square trinomial formula

The perfect square trinomial formula is \(a^2-2ab + b^2=(a - b)^2\). Substituting \(a = x\) and \(b = 8u\) into the formula, we get \((x-8u)^2\).

Answer:

\((x - 8u)^2\)