Find the value of $\left(x-y\right)a+\left(y-z\right)b+\left(z-x\right)c$, if $a=x^2+xy+y^2, b=y^2+yz+z^2, c=x^2+xz+z^2$.

Find the value of $a\left(m+n\right)+b\left(n+l\right)+c\left(l+m\right)$, if $a=lx+my+n, b=mx+ny+l, c=nx+ly+m$.

The product of $\left(x^2+x\right)$ and $\left(x-1\right)$ is $\left(x^3-x\right)$

If $\left(x^3-x\right)÷\left(x-1\right)=$$x^k+mx$, then $k+m=$_____

The product of $\left(x^2+x\right)$ and $\left(x-1\right)$ is $\left(x^3-x\right)$, then fill in the blank when $\left(x^3-x\right)÷\left(x^2+x\right)=$_____

If the product of $\left(x-6\right)$ and $\left(x-3\right)$ is $k{x}^2+lx+m$, then$k+l+m=$  _____.

The product of $\left(x-6\right)$ and $\left(x-3\right)$ is $x^2-9x+18$

Then, fill in the blank when $\left(x^2-9x+18\right)÷\left(x-3\right)=$_____

The product of $\left(x-6\right)$ and $\left(x-3\right)$ is $\left(x^2-9x+18\right)$

Then fill in the blank when $\left(x^2-9x+18\right)÷\left(x-6\right)=$_____.

If The product of $\left(1-2c\right)$ and $\left(1-3c\right)$ is $m+lc+k{c}^2$, then $k+l+m=$ _____.

The product of $\left(1-2c\right)$ and $\left(1-3c\right)$ is $\left(1-5c+6c^2\right)$

Then fill in the blank when $\left(1-5c+6c^2\right)÷\left(1-2c\right)=$_____.