Find the remainder when $x^{3}+3 x^{2}+3 x+1$ is divided by $x$.
$5$
$4$
$1$
$0$
Verify : $x^{3}+y^{3}=(x+y)\left(x^{2}-x y+y^{2}\right)$
Evaluate $105 \times 106$ without multiplying directly.
Use suitable identities to find the products : $(3-2 x)(3+2 x)$
Use suitable identities to find the products : $(x+8)(x-10)$
Factorise the following using appropriate identities :$x^{2}-\frac{y^{2}}{100}$