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

Problem

16*x^2−24*x*y+9*y^2

Solution

1. Identify the expression as a trinomial and check if the first and last terms are perfect squares.

2. Recognize that 16*x^2 is (4*x)^2 and 9*y^2 is (3*y)^2

3. Verify the middle term by checking if it matches the pattern 2*a*b for a perfect square trinomial (a−b)^2=a^2−2*a*b+b^2

4. Calculate $2(4x)(3y) = 24xy$, which matches the middle term of the expression.

5. Apply the perfect square trinomial formula (a−b)^2 where a=4*x and b=3*y

Final Answer

16*x^2−24*x*y+9*y^2=(4*x−3*y)^2

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