Factor 9x^2-24xy+16y^2

Problem

9*x2−24*x*y+16*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 root of the first term 9*x2 which is 3*x

3. Determine the square root of the last term 16*y2 which is 4*y

4. Verify the middle term by calculating 2*(3*x)*(4*y) which equals 24*x*y

5. Apply the perfect square trinomial formula (a−b)2=a2−2*a*b+b2 using a=3*x and b=4*y

Final Answer

9*x2−24*x*y+16*y2=(3*x−4*y)2

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