Question

factor the binomial completely.

\\x^2 - 225y^2\\

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

a. \\(x^2 - 225y^2 = \\) (factor completely.)
b. the polynomial is prime.

Explanation:

⚡ Using what you learned: factoring special products

Step 1: Identify the pattern

The given binomial is:

$$ x^2 - 225y^2 $$

This fits the difference of squares pattern:

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

Step 2: Rewrite as perfect squares

Identify \( a \) and \( b \):

$$ a^2 = x^2 \implies a = x $$

$$ b^2 = 225y^2 \implies b = 15y $$

Rewrite the expression:

$$ (x)^2 - (15y)^2 $$

Step 3: Apply the formula

Substitute \( a = x \) and \( b = 15y \) into the difference of squares formula:

$$ (x - 15y)(x + 15y) $$

Answer:

A. \( x^2 - 225y^2 = (x - 15y)(x + 15y) \)