Question

identify the pattern
1 ( x^2 - 20x + 100 )

Explanation:

Step1: Analyze the quadratic expression

The given expression is \(x^{2}-20x + 100\). We can check if it's a perfect square trinomial. A perfect square trinomial has the form \(a^{2}-2ab + b^{2}=(a - b)^{2}\).

Step2: Identify \(a\) and \(b\)

Here, \(a = x\) (since \(a^{2}=x^{2}\)), and \(2ab = 20x\). Substituting \(a=x\) into \(2ab = 20x\), we get \(2\times x\times b=20x\). Dividing both sides by \(2x\) (assuming \(x
eq0\)), we find \(b = 10\). Now, check \(b^{2}\): \(b^{2}=10^{2}=100\), which matches the constant term.

Step3: Factor the expression

Using the perfect square trinomial formula, \(x^{2}-20x + 100=(x - 10)^{2}\).

Answer:

The factored form of \(x^{2}-20x + 100\) is \((x - 10)^{2}\) (it's a perfect square trinomial pattern).