Factor u^2v^2-225

Problem

u^2*v^2−225

Solution

1. Identify the expression as a difference of two squares, which follows the pattern a^2−b^2

2. Rewrite each term as a perfect square to find the values of a and b

3. Determine a by taking the square root of the first term: √(,u^2*v^2)=u*v

4. Determine b by taking the square root of the second term: √(,225)=15

5. Apply the formula for the difference of squares, a^2−b^2=(a−b)*(a+b) using a=u*v and b=15

Final Answer

u^2*v^2−225=(u*v−15)*(u*v+15)

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