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

Problem

4*x^2−12*x*y+9*y^2

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*x^2=(2*x)^2

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

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

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*x^2−12*x*y+9*y^2=(2*x−3*y)^2

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