Question

factor $x^2 - 20x + 100$. the factored form is \boxed{}

Explanation:

Step1: Recall the perfect square trinomial formula

The perfect square trinomial formula is $a^2 - 2ab + b^2=(a - b)^2$.

Step2: Identify \(a\) and \(b\) in the given trinomial

For the trinomial $x^2 - 20x + 100$, we have $a = x$ (since $x^2=(x)^2$), and $2ab = 20x$. Substituting $a = x$ into $2ab = 20x$, we get $2\times x\times b = 20x$. Solving for $b$, we divide both sides by $2x$ (assuming $x
eq0$), so $b=\frac{20x}{2x}=10$. Also, $b^2 = 10^2 = 100$, which matches the constant term in the trinomial.

Step3: Apply the perfect square trinomial formula

Using the formula $a^2 - 2ab + b^2=(a - b)^2$ with $a = x$ and $b = 10$, we get $x^2 - 20x + 100=(x - 10)^2$.

Answer:

$(x - 10)^2$