question\nfactor completely.\n81x² - 1

Explanation:

Step1: Recognize difference - of - squares

The expression $81x^{2}-1$ is in the form $a^{2}-b^{2}$, where $a = 9x$ and $b = 1$. Since $81x^{2}=(9x)^{2}$ and $1 = 1^{2}$.

Step2: Apply difference - of - squares formula

The formula for $a^{2}-b^{2}$ is $(a + b)(a - b)$. Substituting $a = 9x$ and $b = 1$ gives $(9x+1)(9x - 1)$.

Answer:

$(9x + 1)(9x - 1)$