Factor 25x^2-30x+9

Problem

25*x^2−30*x+9

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x^2+b*x+c

2. Recognize that the first term 25*x^2 is a perfect square, (5*x)^2 and the last term 9 is a perfect square, 3^2

3. Check if the middle term fits the pattern for a perfect square trinomial a^2−2*a*b+b^2 where a=5*x and b=3

4. Verify the middle term by calculating 2*a*b

2*(5*x)*(3)=30*x

5. Apply the formula for a perfect square trinomial (a−b)^2

(5*x−3)^2

Final Answer

25*x^2−30*x+9=(5*x−3)^2

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