Questions: Factor. x^2+10x+25

Solution Steps

The given expression \(x^2 + 10x + 25\) is a perfect square trinomial because the first term (\(x^2\)) and the last term (25) are perfect squares, and the middle term (\(10x\)) is twice the product of the square roots of the first and last terms. Specifically, \(\sqrt{x^2} = x\), \(\sqrt{25} = 5\), and \(2(x)(5) = 10x\).

A perfect square trinomial of the form \(a^2 + 2ab + b^2\) factors as \((a+b)^2\). In our case, \(a=x\) and \(b=5\), so \(x^2 + 10x + 25\) factors as \((x+5)^2\).

Final Answer