EXERCISE

Carry out the multiplication of the expression in each of the following pairs:
$4\mathrm{p}, \mathrm{q}+\mathrm{r}$

Carry out the multiplication of the expression in the following pairs:
$\mathrm{ab}, \mathrm{a}-\mathrm{b}$

Carry out the multiplication of the expression in the following pair:

$\mathrm{a}+\mathrm{b}, 7{\mathrm{a}}^2\mathrm{b}$

Simplify  $\mathrm{a}\left({\mathrm{a}}^2+\mathrm{a}+1\right)+5$ and find the value for  $\mathrm{a}=-1$.
 

On adding $\mathrm{p}(\mathrm{p}-\mathrm{q}), \mathrm{q}(\mathrm{q}–\mathrm{r})$and$\mathrm{r}(\mathrm{r}–\mathrm{p})$if we get $p^2+q^2+r^2-pq-qr+k$.

Then find the value of $k$.

On adding $2\mathrm{x}(\mathrm{z}–\mathrm{x}–\mathrm{y}) \mathrm{and} 2\mathrm{y}(\mathrm{z}–\mathrm{y}–\mathrm{x})$ if we get $-2x^2-2y^2-4xy+kz+2zx$. 

Then find the value of $k$.

On subtracting $3\mathrm{l}(\mathrm{l}–4\mathrm{m}+5\mathrm{n})$ from $4\mathrm{l}(10\mathrm{n}–3\mathrm{m}+2\mathrm{l})$ if we get $k{l}^2+25\ln$. 

Then find the value of $k$.

On subtracting $3\mathrm{a}(\mathrm{a}+\mathrm{b}+\mathrm{c})–2\mathrm{b}(\mathrm{a}–\mathrm{b}+\mathrm{c})$ from $4\mathrm{c}(–\mathrm{a}+\mathrm{b}+\mathrm{c})$ if we get $-3a^2-2b^2+4c^2-ab+kbc-7ac$. 

Then find the value of $k$.