Question

How do you simplify $p\left( p-q \right)+q\left( q-r \right)+r\left( r-p \right)$ ?

Answer 1

Hint: In this question we have been asked to simplify the given expression $p\left( p-q \right)+q\left( q-r \right)+r\left( r-p \right)$ . For doing that we should perform basic arithmetic simplification operations like multiplication and subtraction between similar terms. Firstly we will multiply $p$ and $p-q$ then we will have $\Rightarrow {{p}^{2}}-pq+q\left( q-r \right)+r\left( r-p \right)$ .

Complete step by step solution:
Now considering from the question we have been asked to simplify the given expression $p\left( p-q \right)+q\left( q-r \right)+r\left( r-p \right)$ .
For doing that we should perform basic arithmetic simplification operations like multiplication and subtraction between similar terms.
Firstly we will multiply $p$ and $p-q$ then we will have $\Rightarrow {{p}^{2}}-pq+q\left( q-r \right)+r\left( r-p \right)$ .
Now we will multiply $q$ and $q-r$ after doing that we will have $\Rightarrow {{p}^{2}}-pq+{{q}^{2}}-qr+r\left( r-p \right)$ .
Similarly now we will perform multiplication arithmetic operation between $r$ and $r-p$ then we will have $\Rightarrow {{p}^{2}}-pq+{{q}^{2}}-qr+{{r}^{2}}-pr$ .
Therefore we can conclude that the simplified or reduced form of the given expression $p\left( p-q \right)+q\left( q-r \right)+r\left( r-p \right)$ is given as ${{p}^{2}}-pq+{{q}^{2}}-qr+{{r}^{2}}-pr$ .

Note: While answering questions of this type we should be sure with the calculations that we perform in between. This is a very simple and easy question and can be answered in a short span of time accurately. Very few mistakes are possible in questions of this type. Someone can perform a calculation mistake by just over seeing it. For example someone can write it as ${{p}^{2}}-pq+{{q}^{2}}-qr+{{r}^{2}}-2pr$ . This will lead them to end up having a wrong conclusion. Similarly there may be any other calculation mistake possibly. For example someone can write it as ${{p}^{2}}-pq+{{q}^{2}}-2qr+{{r}^{2}}-pr$. So be careful while answering this type of question.