Factorise : $2 x^{2}+y^{2}+8 z^{2}-2 \sqrt{2} x y+4 \sqrt{2} y z-8 x z$
Write the following cubes in expanded form : $\left[x-\frac{2}{3} y\right]^{3}$
Find the zero of the polynomial : $p(x)=c x+d, \,c \neq 0, \,c,\,d$ are real numbers.
If $x+y+z=0,$ show that $x^{3}+y^{3}+z^{3}=3 x y z$.
What are the possible expressions for the dimensions of the cuboids whose volumes are given below?$\boxed{\rm {Volume}\,:12 k y^{2}+8 k y-20 k}$