Factor 25x^2+30x+9

Problem

25*x2+30*x+9

Solution

1. Identify the structure of the quadratic expression, which is in the form a*x2+b*x+c

2. Recognize that the first term 25*x2 is a perfect square, (5*x)2

3. Recognize that the last term 9 is a perfect square, 3

4. Check if the middle term 30*x fits the pattern 2*a*b for a perfect square trinomial (a+b)2

5. Verify the calculation: 2⋅(5*x)⋅3=30*x

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

Final Answer

25*x2+30*x+9=(5*x+3)2

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