Factor x^2+2xy+y^2

Problem

x^2+2*x*y+y^2

Solution

1. Identify the structure of the expression as a trinomial of the form a^2+2*a*b+b^2

2. Recognize the pattern for a perfect square trinomial, which follows the identity (a+b)^2=a^2+2*a*b+b^2

3. Assign the variables where a=x and b=y

4. Rewrite the expression in its factored form as the square of a binomial.

Final Answer

x^2+2*x*y+y^2=(x+y)^2

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