Math Snap

STEP 1

1. A perfect square trinomial takes the form $(a-b)^2 = a^2 - 2ab + b^2$.
2. We need to determine if the given polynomial fits this form.
3. If it does, we will factor it; otherwise, we will state that it is prime.

STEP 2

1. Identify the structure of the polynomial.
2. Determine if the polynomial is a perfect square trinomial.
3. Factor the polynomial if it is a perfect square trinomial.

STEP 3

Identify the terms in the polynomial $x^{2}-20xy+100y^{2}$.
- The first term is $x^2$, which is a perfect square $(x)^2$.
- The last term is $100y^2$, which is a perfect square $(10y)^2$.

STEP 4

Check if the middle term fits the form $-2ab$, where $a = x$ and $b = 10y$.
- Calculate $2ab = 2 \times x \times 10y = 20xy$.
The middle term $-20xy$ matches $-2ab$.

Since the polynomial fits the form of a perfect square trinomial, factor it as:
$$(x - 10y)^2$$ Thus, the factored form of the polynomial is:
$$x^{2}-20xy+100y^{2} = (x - 10y)^2$$