1. The problem is to verify the identity for the square of a sum, which states that $$(a+b)^2 = a^2 + 2ab + b^2.$$\n\n2. Start with the left-hand side (LHS): $$(a+b)^2.$$\n\n3. Expand the square using the distributive property: $$(a+b)(a+b) = a(a+b) + b(a+b).$$\n\n4. Distribute $a$ and $b$: $$a^2 + ab + ba + b^2.$$\n\n5. Since multiplication is commutative, $ab = ba$, so combine like terms: $$a^2 + 2ab + b^2.$$\n\n6. This matches the right-hand side (RHS) of the identity, confirming that $$(a+b)^2 = a^2 + 2ab + b^2.$$\n\nTherefore, the identity is proven.