Question

factor.

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

Explanation:

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<reasoning>

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 \(b = 5x\):
\[ (3y - 5x)(3y + 5x) \]
</reasoning>

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

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Answer:

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<reasoning>

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 \(b = 5x\):
\[ (3y - 5x)(3y + 5x) \]
</reasoning>

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

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