Factor 36x^2-84xy+49y^2

Problem

36*x2−84*x*y+49*y2

Solution

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

2. Determine the square root of the first term 36*x2 which is 6*x

3. Determine the square root of the last term 49*y2 which is 7*y

4. Verify the middle term by calculating 2*a*b which is 2(6x)(7y) = 84xy$.

5. Apply the perfect square trinomial formula (a−b)2=a2−2*a*b+b2

Final Answer

36*x2−84*x*y+49*y2=(6*x−7*y)2

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