Expand Square 39A082

1. **Problem Statement:** Expand the square of the binomial $$(x+2)^2$$ and understand why the expansion is $x^2 + 4x + 4$ and not just $x^2 + 4$.\n\n2. **Formula Used:** The formula for the square of a binomial is:\n$$ (a+b)^2 = a^2 + 2ab + b^2 $$\nwhere $a = x$ and $b = 2$.\n\n3. **Applying the formula:**\n$$ (x+2)^2 = x^2 + 2 \cdot x \cdot 2 + 2^2 $$\n\n4. **Simplify each term:**\n$$ x^2 + 4x + 4 $$\n\n5. **Why not just $x^2 + 4$?**\nIf you only write $x^2 + 4$, you are missing the middle term $4x$, which comes from the product of $2ab$ in the formula. This term is important because when you expand $(x+2)(x+2)$, you multiply $x$ by $2$ and $2$ by $x$, giving $4x$.\n\n6. **Intermediate step showing cancellation if you tried to remove the middle term (incorrect):**\n$$ x^2 + \cancel{4x} + 4 \quad \text{(Removing $4x$ is incorrect)} $$\n\n7. **Conclusion:** Always use the full binomial square formula to expand $(x+2)^2$ to get $x^2 + 4x + 4$. Omitting the middle term $4x$ is a mistake.