Factor a^2+2ab+b^2

Problem

a2+2*a*b+b2

Solution

1. Identify the structure of the expression as a trinomial with three terms.

2. Recognize that the first term a2 is the square of a and the last term b2 is the square of b

3. Check the middle term to see if it fits the pattern 2⋅(first root)⋅(second root) which is 2*a*b

4. Apply the formula for a perfect square trinomial, which states x2+2*x*y+y2=(x+y)2

Final Answer

a2+2*a*b+b2=(a+b)2

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