Factor 4x^2+20x+25

Problem

4*x2+20*x+25

Solution

1. Identify the structure of the quadratic expression a*x2+b*x+c where a=4 b=20 and c=25

2. Recognize that the first term 4*x2 is a perfect square, (2*x)2 and the last term 25 is a perfect square, 5

3. Check if the middle term 20*x fits the pattern 2*a*b for a perfect square trinomial (a+b)2

4. Verify the middle term calculation:

2*(2*x)*(5)=20*x

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

6. Substitute a=2*x and b=5 into the formula.

Final Answer

4*x2+20*x+25=(2*x+5)2

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