Question

determine if the following equation is an identity (x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2zxA) this is an identity because equation is trueB) this is an identity because the equation is not trueC) this is not an identity because equation is trueD) this is not an identity because equation is not true

Answer 1

$\begin{gathered} (x+y+z)^2=(x+y+z)(x+y+z) \\ =x(x+y+z)+y(x+y+z)+z(x+y+z) \\ =(x^2+xy+xz)+(xy+y^2+yz)+(xz+yz+z^2) \\ =x^2+y^2+z^2+2xy+2yz+2zx \end{gathered}$

So the equation is an identity becase the equation is true!