Simplify (x+y)^2

Problem

(x+y)2

Solution

1. Identify the expression as a binomial squared, which follows the algebraic identity (a+b)2=a2+2*a*b+b2

2. Expand the expression by multiplying the binomial by itself: (x+y)*(x+y)

3. Distribute each term in the first set of parentheses by each term in the second set of parentheses using the FOIL method (First, Outer, Inner, Last).

x(x)+x(y)+y(x)+y(y)

4. Multiply the individual terms.

x2+x*y+y*x+y2

5. Combine the like terms x*y and y*x noting that x*y=y*x due to the commutative property of multiplication.

x2+2*x*y+y2

Final Answer

(x+y)2=x2+2*x*y+y2

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