Factor 9x^2-12xy+4y^2

Problem

9*x2−12*x*y+4*y2

Solution

1. Identify the structure of the expression as a potential perfect square trinomial of the form a2−2*a*b+b2

2. Determine the square roots of the first and last terms to find a and b

3. Calculate a from the first term:

√(,9*x2)=3*x

4. Calculate b from the last term:

√(,4*y2)=2*y

5. Verify the middle term by calculating 2*a*b

2*(3*x)*(2*y)=12*x*y

6. Apply the formula for a perfect square trinomial a2−2*a*b+b2=(a−b)2 using a=3*x and b=2*y

Final Answer

9*x2−12*x*y+4*y2=(3*x−2*y)2

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