Question

find the product and answer​

Answer 1

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Answer 2

To solve it, we have to be familiar with the identity given below.

$\large (a+b+c)(a^2+b^2+c^2-ab-bc-ca)=a^3+b^3+c^3-3abc$

Taking,

$a=x\\ \\ b=y\\ \\ c=-z$

we get that,

$\begin{aligned}&(x+y-z)(x^2+y^2+z^2-xy+yz+xz)\\ \\ \Longrightarrow\ \ &(x+y+(-z))(x^2+y^2+(-z)^2-xy-(-yz)-(-zx))\\ \\ \Longrightarrow\ \ &(a+b+c)(a^2+b^2+c^2-ab-bc-ca)\\ \\ \Longrightarrow\ \ &a^3+b^3+c^3-3abc\\ \\ \Longrightarrow\ \ &x^3+y^3+(-z)^3-3xy(-z)\\ \\ \Longrightarrow\ \ &x^3+y^3-z^3+3xyz\end{aligned}$

Hence expanded it and found out the product!