Question

factor completely. $s^2 - 10s + 25$

Explanation:

Step1: Identify the form

The quadratic expression \( s^2 - 10s + 25 \) is a perfect square trinomial. The general form of a perfect square trinomial is \( a^2 - 2ab + b^2=(a - b)^2 \).

Step2: Match the terms

For \( s^2 - 10s + 25 \), we have \( a = s \) (since \( a^2=s^2 \)), and \( 2ab = 10s \). Substituting \( a = s \) into \( 2ab = 10s \), we get \( 2\times s\times b=10s \), which simplifies to \( b = 5 \) (dividing both sides by \( 2s \)). Also, \( b^2 = 25 \) (since \( 5^2 = 25 \)), which matches the constant term.

Step3: Factor the expression

Using the perfect square trinomial formula \( a^2 - 2ab + b^2=(a - b)^2 \) with \( a = s \) and \( b = 5 \), we get \( s^2 - 10s + 25=(s - 5)^2 \).

Answer:

\((s - 5)^2\)