Question

factor the following.
100y² + 20y + 1 - x²
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. 100y² + 20y + 1 - x² =
b. 100y² + 20y + 1 - x² is prime.

Explanation:

Step1: Recognize perfect - square trinomial

Notice that $100y^{2}+20y + 1=(10y + 1)^{2}$ since $(a + b)^{2}=a^{2}+2ab + b^{2}$, where $a = 10y$ and $b = 1$. So the expression becomes $(10y + 1)^{2}-x^{2}$.

Step2: Apply difference - of - squares formula

The difference - of - squares formula is $a^{2}-b^{2}=(a + b)(a - b)$. Here $a=10y + 1$ and $b = x$. So $(10y + 1)^{2}-x^{2}=(10y+1 + x)(10y + 1-x)$.

Answer:

A. $(10y + 1 + x)(10y+1 - x)$