Question

factor

\\ -81r^2 + 1 \\

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. \\( -81r^2 + 1 = \\) (factor completely.)

b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring special products

Step 1: Rewrite the expression

$$ -81r^2 + 1 = 1 - 81r^2 $$

Step 2: Identify the difference of squares

$$ 1^2 - (9r)^2 $$

Step 3: Apply the factoring formula

$$ a^2 - b^2 = (a - b)(a + b) $$

$$ (1 - 9r)(1 + 9r) $$

Answer:

A. \( -81r^2 + 1 = (1 - 9r)(1 + 9r) \)