which expression is equivalent to 100n² - 1?\n(10n)² - (1)²\n(10n²)² - (1)²\n(50n)² - (1)²\n(50n²)² - (1)²

Explanation:

Step1: Analyze the square - root of 100n²

We know that $\sqrt{100n^{2}} = 10n$ since $\sqrt{100}=10$ and $\sqrt{n^{2}}=n$. And $\sqrt{1}=1$.

Step2: Rewrite the expression

The expression $100n^{2}-1$ can be written as $(10n)^{2}-(1)^{2}$ according to the rule $a^{2}-b^{2}$ where $a = 10n$ and $b = 1$.

Answer:

$(10n)^{2}-(1)^{2}$