Question

question
factor.
$x^2 + 10x + 25$

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 the expression \(x^2+10x + 25\), we have \(a = x\) (since \(x^2=a^2\)), and \(2ab = 10x\). Substituting \(a=x\) into \(2ab = 10x\), we get \(2\times x\times b=10x\), which simplifies to \(2b = 10\), so \(b = 5\). Also, \(b^2=25\) (since \(5^2 = 25\)), which matches the constant term.

Step3: Apply the formula

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

Answer:

\((x + 5)^2\)