Factor x^2+20x+100

Problem

x2+20*x+100

Solution

1. Identify the structure of the quadratic expression x2+20*x+100 which is in the form a*x2+b*x+c

2. Recognize that the first term x2 is a perfect square of x and the last term 100 is a perfect square of 10

3. Check if the middle term 20*x fits the pattern 2*a*b for a perfect square trinomial a2+2*a*b+b2

4. Verify the calculation 2⋅x⋅10=20*x which matches the middle term.

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

Final Answer

x2+20*x+100=(x+10)2

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