Question

factor.

\\9y^2 - 25x^2\\

Explanation:

Identify the structure of the binomial

The given expression is:

$$ 9y^2 - 25x^2 $$

Both terms are perfect squares separated by a subtraction sign, which represents a difference of squares.

Express each term as a perfect square

We rewrite each term in the form \(a^2 - b^2\):

$$ 9y^2 = (3y)^2 $$

$$ 25x^2 = (5x)^2 $$

Thus, the expression becomes:

$$ (3y)^2 - (5x)^2 $$

Apply the difference of squares formula

The difference of squares formula is:

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

Substituting \(a = 3y\) and \(b = 5x\):

$$ (3y - 5x)(3y + 5x) $$

Answer:

Factor.
\(9y^2 - 25x^2 = \) <blank>\((3y - 5x)(3y + 5x)\)</blank>