Question

factor $x^2 - 30x + 225$. the factored form is \boxed{}

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 quadratic expression $x^2 - 30x + 225$, we have $a = x$ (since $x^2=(x)^2$), and we need to find \(b\) such that $2ab = 30x$. Substituting \(a=x\) into $2ab = 30x$, we get $2\times x\times b = 30x$. Dividing both sides by $2x$ (assuming $x
eq0$), we find $b = 15$. Also, $b^2 = 15^2 = 225$, which matches the constant term in the given quadratic expression.

Step3: Apply the perfect square formula

Using the perfect square trinomial formula $a^2 - 2ab + b^2=(a - b)^2$ with $a = x$ and $b = 15$, we can factor $x^2 - 30x + 225$ as $(x - 15)^2$.

Answer:

$(x - 15)^2$