Question

factor the following binomial completely.

\\x^2y^2 - 36\\

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

a. \\(x^2y^2 - 36 = \\) (factor completely.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring special products

Step 1: Identify the pattern

The binomial is a difference of two perfect squares:

$$ x^2y^2 - 36 = (xy)^2 - 6^2 $$

Step 2: Apply the difference of squares formula

Using the formula \( a^2 - b^2 = (a - b)(a + b) \) where \( a = xy \) and \( b = 6 \):

$$ (xy)^2 - 6^2 = (xy - 6)(xy + 6) $$

Answer:

A. \( x^2y^2 - 36 = (xy - 6)(xy + 6) \)