Simplify:

${\left(\mathrm{x}+1\right)}^2-{\left(\mathrm{x}-1\right)}^2$

${\left(7-\mathrm{y}\right)}^2+14\mathrm{y}=\mathrm{a}+\mathrm{by}+{\mathrm{cy}}^2$. Find $a+b+c$.

If the simplified form of ${\left({\mathrm{a}}^2+{\mathrm{b}}^2\right)}^2-2{\mathrm{a}}^2{\mathrm{b}}^2$ is $a^n+b^n$ then find the value of $n$.

On expanding ${\left(\frac{1}{9}{x}^3+3\right)}^2$ we get $\frac{1}{81}{\mathrm{x}}^6+\frac{2}{3}{\mathrm{x}}^3+k$, then find the value of $k$.

On expanding ${\left(\frac{3}{8}\mathrm{a}-14\mathrm{b}\right)}^2$ we get $\frac{9}{64}{\mathrm{a}}^2-\frac{21}{2}\mathrm{ab}+k{\mathrm{b}}^2$, then find the value of $k$.

If the expanded form of ${\left(\frac{1}{5}{\mathrm{b}}^2-5\mathrm{c}\right)}^2$ is $m{b}^4+n{c}^4+p{b}^{2}c$, then find the value of $m+n+p$ [as an improper fraction].

If the expanded form of ${\left(2x^2+\frac{1}{3x^2}\right)}^2$ is $a{x}^4+\frac{b}{x^4}+c$, then find the value of $a+b+c$ [as an improper fraction].

Using the identity of square of a binomial, evaluate the following:

${\left(102\right)}^2$

Using the identity of square of a binomial, evaluate the following:

${\left(53\right)}^2$