Question

factor.

( v^2 - 16v + 64 )

Explanation:

Step1: Recall perfect square formula

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

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

For the trinomial \(v^2-16v + 64\), we have:

• The first term \(v^2=(v)^2\), so \(a = v\).
• The last term \(64 = 8^2\), so \(b = 8\).
• Now check the middle term: \(2ab=2\times v\times8 = 16v\), which matches the middle term (with a negative sign, so it's \(-2ab=-16v\)).

Step3: Apply the perfect square formula

Using the formula \(a^2 - 2ab + b^2=(a - b)^2\) with \(a = v\) and \(b = 8\), we get:
\(v^2-16v + 64=(v - 8)^2\)

Answer:

\((v - 8)^2\)