### Theory:

Now we have to find out the values of algebraic expressions using the given variables.
Steps to find the value of the algebraic expression:

Step $$1$$: Understand the problem first and then fix the variable and write the algebraic expression.

Step $$2$$: Substitute each variable by the given numerical value to get an arithmetical expression.

Step $$3$$: Try to solve or simplify the arithmetical expression by the BIDMAS method.

Step $$4$$: Now, the final value you obtained is the required value of the expression.
Example:
Question I)

Consider the algebraic expression $13m-9n-8$ and the value of $$m=$$ 12 and $$n=$$ 4.

Now substitute the values of $$m$$ and $$n$$, we get

$\begin{array}{l}=13\left(12\right)-9\left(4\right)-8\\ \\ =156-36-8\\ \\ =156-44\\ \\ =112\end{array}$

Therefore, the value of the algebraic expression $13m-9n-8$ $$=$$ 112.

Question II)

Consider the algebraic expression ${m}^{2}-4{n}^{2}+4$ with the value of $$m=$$ 12 and $$n=$$ 4.

Now substitute the values of $$m$$ and $$n$$, we get

$\begin{array}{l}={12}^{2}-4\phantom{\rule{0.147em}{0ex}}\left({4}^{2}\right)+4\\ \\ =144-4\phantom{\rule{0.147em}{0ex}}\left(16\right)+4\\ \\ =144-64+4\\ \\ =148-64\\ \\ =84\end{array}$

Therefore, the value of the algebraic expression ${m}^{2}-4{n}^{2}+4$ $$=$$ 84.

Question III)

Consider the algebraic expression is $2{m}^{2}-{8n}^{2}+13$ with the value of $$m=$$ 12 and $$n=$$ 4.

Now substitute the values of $$m$$ and $$n$$, we get

$\begin{array}{l}=\phantom{\rule{0.147em}{0ex}}2\left({12}^{2}\right)\phantom{\rule{0.147em}{0ex}}-8\left({4}^{2}\right)+13\\ \\ =\phantom{\rule{0.147em}{0ex}}2\left(144\right)\phantom{\rule{0.147em}{0ex}}-8\phantom{\rule{0.147em}{0ex}}\left(16\right)\phantom{\rule{0.147em}{0ex}}+13\\ \\ =\phantom{\rule{0.147em}{0ex}}288\phantom{\rule{0.147em}{0ex}}-128+13\\ \\ =301-128\\ \\ =147\end{array}$

Therefore, the value of the algebraic expression $2{m}^{2}-{8n}^{2}+13$ $$=$$ 147.