Factor a^2+2ab+b^2

Problem

a^2+2*a*b+b^2

Solution

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

2. Recognize that the first term a^2 is the square of a and the last term b^2 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 x^2+2*x*y+y^2=(x+y)^2

Final Answer

a^2+2*a*b+b^2=(a+b)^2

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