Simplify (a+b)^2

Problem

(a+b)2

Solution

1. Identify the expression as a binomial squared, which follows the algebraic identity (x+y)2=x2+2*x*y+y2

2. Expand the expression by multiplying the binomial by itself: (a+b)*(a+b)

3. Distribute each term in the first binomial to each term in the second binomial using the FOIL method (First, Outer, Inner, Last).

a(a)+a(b)+b(a)+b(b)

4. Multiply the terms to get the individual products.

a2+a*b+b*a+b2

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

a2+2*a*b+b2

Final Answer

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

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