What will be the value of $r^2+p^2+s^2-rp-ps-rs$ when $r=4$, $p=2$, and $s=8$?

Given expression:
$$E=r^2+p^2+s^2-rp-ps-rs$$
We can use the algebraic identity:
$$r^2+p^2+s^2-rp-ps-rs=\frac{1}{2}\left[(r-p{)}^2+(p-s{)}^2+(s-r{)}^2\right]$$
Substitute the given values $r=4$, $p=2$, and $s=8$:
$$r-p=4-2=2$$
$$p-s=2-8=-6$$
$$s-r=8-4=4$$
Now, substitute these differences back into the identity:
$$E=\frac{1}{2}\left[(2{)}^2+(-6{)}^2+(4{)}^2\right]$$
$$E=\frac{1}{2}[4+36+16]$$
$$E=\frac{1}{2}[56]$$
$$E=28$$