Factor x^2+10x+25

Problem

x^2+10*x+25

Solution

1. Identify the structure of the quadratic expression x^2+10*x+25 which is in the form a*x^2+b*x+c

2. Recognize that the first term x^2 is a perfect square of x and the last term 25 is a perfect square of 5

3. Check if the middle term 10*x matches the pattern 2*a*b for a perfect square trinomial (a+b)^2

4. Verify the calculation: 2⋅x⋅5=10*x

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

Final Answer

x^2+10*x+25=(x+5)^2

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