Which identity is true? (x + y + z)^2 = ...

1. Expand the expression: We need to expand the left side of the equation, $(x + y + z)^2$. This can be done by multiplying $(x + y + z)$ by itself.
$$(x + y + z)^2 = (x + y + z)(x + y + z)$$
2. Distribute the terms: Apply the distributive property (or FOIL method extended) to multiply the two trinomials.
$$x(x + y + z) + y(x + y + z) + z(x + y + z)$$
3. Perform the multiplication: Multiply each term in the first trinomial by each term in the second trinomial.
$$x^2 + xy + xz + yx + y^2 + yz + zx + zy + z^2$$
4. Group like terms: Combine terms that have the same variables raised to the same powers.
$$x^2 + y^2 + z^2 + (xy + yx) + (yz + zy) + (xz + zx)$$
5. Simplify like terms: Since multiplication is commutative ($xy = yx$, $yz = zy$, $xz = zx$), we can combine these terms.
$$x^2 + y^2 + z^2 + 2xy + 2yz + 2xz$$
6. Compare with the options: Now, compare the expanded form with the given options. The correct identity is the one that matches our expansion.