Factor 25x^2+20x+4

Problem

25*x^2+20*x+4

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, as (5*x)^2=25*x^2

3. Recognize that the last term 4 is a perfect square, as 2^2=4

4. Check if the middle term 20*x matches the pattern for a perfect square trinomial a^2+2*a*b+b^2 where a=5*x and b=2

5. Verify the middle term calculation:

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

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

7. Substitute the values a=5*x and b=2 into the factored form.

Final Answer

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

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