Question

factor completely. 16k² - 40k + 25

Explanation:

Step1: Identify the form

Notice that \(16k^2=(4k)^2\) and \(25 = 5^2\), and the middle term \(-40k=-2\times4k\times5\). So the expression is a perfect square trinomial of the form \(a^2 - 2ab + b^2=(a - b)^2\).

Step2: Apply the formula

Here, \(a = 4k\) and \(b = 5\). Substituting into the formula \((a - b)^2=a^2-2ab + b^2\), we get \((4k - 5)^2\).

Answer:

\((4k - 5)^2\)