Which explanation correctly demonstrates why $(a+b{)}^2\ne a^2+b^2$?

• A. Expanding $(a+b)(a+b)$ using FOIL yields $a^2+ab+ab+b^2$; combining the middle terms produces $a^2+2ab+b^2$.
• B. The Power of a Product rule states that exponents distribute over addition, but a correction factor of $2ab$ must be added manually.
• C. Squaring a binomial eliminates the cross-terms through symmetry, meaning $a^2+b^2$ is the simplified form for all real numbers.
• D. Multiplying $(a+b)$ by $2$ transforms the expression into $2a+2b$, which simplifies to $a^2+b^2$ after applying the Power Rule.

Answer: (A)