Factor 9x^2+30x+25

Problem

9*x2+30*x+25

Solution

1. Identify the structure of the quadratic expression a*x2+b*x+c where a=9 b=30 and c=25

2. Recognize that the first term 9*x2 is a perfect square, (3*x)2 and the last term 25 is a perfect square, 5

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

4. Verify the calculation 2⋅(3*x)⋅5=30*x which matches the middle term.

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

Final Answer

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

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