Factor 36x^2+60x+25

Problem

36*x2+60*x+25

Solution

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

2. Check for a perfect square trinomial by looking at the first and last terms.

3. Recognize that the first term is a perfect square: 36*x2=(6*x)2

4. Recognize that the last term is a perfect square: 25=5

5. Verify the middle term by checking if it equals 2*(6*x)*(5)

6. Calculate 2⋅6*x⋅5=60*x which matches the middle term of the expression.

7. Apply the perfect square trinomial formula a2+2*a*b+b2=(a+b)2 where a=6*x and b=5

Final Answer

36*x2+60*x+25=(6*x+5)2

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