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

Problem

4*x2−12*x*y+9*y2

Solution

1. Identify the structure of the expression as a trinomial that may be a perfect square.

2. Recognize the first term as a perfect square: 4*x2=(2*x)2

3. Recognize the last term as a perfect square: 9*y2=(3*y)2

4. Verify the middle term by checking if it equals 2*a*b from the identity (a−b)2=a2−2*a*b+b2

5. Calculate the product: 2(2x)(3y) = 12xy$.

6. Apply the perfect square trinomial formula (a−b)2 where a=2*x and b=3*y

Final Answer

4*x2−12*x*y+9*y2=(2*x−3*y)2

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