Factorise

${\left(a+b\right)}^2-{\left(a-b\right)}^2$

Factorise $a^{2}b-b^3$ and using it, find the value of ${101}^2\times 100-{100}^3$.

By division find out that $\left(x-2\right)$ is a factor of $\left(x^3-8\right)$.

By division find out that $\left(x-y\right)$ is a factor of $\left(x^5-y^5\right)$.

By division find out that $\left(x^2-4x+16\right)$ is a factor of $\left(x^3+64\right)$.

By division find out that $\left(x^4-y^4\right)$ is a factor of $\left(x+y\right)$.

By division find out that $\left(x^3-216\right)$ is a factor of $\left(x-6\right)$.