Factor completely.
$x^2-40x+400$

• A. $(x-20)(x+20)$
• B. $(x-4)(x-100)$
• C. $\(\left\)(x-20\(\right\))^2$
• D. $\(\left\)(x-4\(\right\))\(\left\)(x+100\(\right\))$

Answer: (C)

Verified step by step guidance

1. Identify the general form of a perfect square trinomial, which is either \(a^{2} + 2ab + b^{2}\) or \(a^{2} - 2ab + b^{2}\). These can be factored as \((a + b)^{2}\) or \((a - b)^{2}\) respectively.
2. Look at the given trinomial and check if the first and last terms are perfect squares. For example, check if the first term is a square of some expression \(a^{2}\) and the last term is a square of some expression \(b^{2}\).
3. Verify that the middle term matches \$2ab\( or \)-2ab$ by taking the square roots of the first and last terms and multiplying them by 2, then comparing to the middle term.
4. If the trinomial fits the pattern, write it as the square of a binomial: \((a + b)^{2}\) if the middle term is positive, or \((a - b)^{2}\) if the middle term is negative.
5. If the trinomial does not fit the perfect square pattern, then it is not a perfect square trinomial and cannot be factored as such.