Find Equivalent Expressions for (x+y)²: Perfect Square Expansion

Choose the expression that has the same value as the following:

$(x+y)^2$

To solve this problem, we will use the formula for the square of a sum, which is $(a+b)^2 = a^2 + 2ab + b^2$.

Here, we identify $a = x$ and $b = y$. Thus, our expression $(x+y)^2$ can be expanded as follows:

$(x+y)^2 = x^2 + 2xy + y^2$

Now we will match this expanded form with the given choices.

• Choice 1: $x^2 + y^2$ - This is missing the middle term $2xy$.
• Choice 2: $y^2 + x^2 + 2xy$ - This matches the expanded expression.
• Choice 3: $x^2 + xy + y^2$ - The term $xy$ doesn't match the required $2xy$.
• Choice 4: $x^2 - 2xy + y^2$ - The middle term has an incorrect sign.

Therefore, the expression that is equivalent to $(x+y)^2$ is choice 2: $y^2 + x^2 + 2xy$.