Question

Factorize the given expression: ${p^2}q - p{r^2} - pq + {r^2}$

Answer 1

Hint: In order to solve this question we will use the concept of factorization which can be defined as the breaking or decomposing of an entity into a product of another entity called factors. When the factors are multiplied together the original entity can be obtained.

Complete step-by-step answer:
The given equation for factorization is ${p^2}q - p{r^2} - pq + {r^2}$
Now the given equation is quadratic polynomial with three variables
$ \Rightarrow {p^2}q - p{r^2} - pq + {r^2}$
Rearranging the given equation, so that common terms can be taken out
\[ \Rightarrow \left( {{p^2}q - p{r^2}} \right) - \left( {pq - {r^2}} \right)\]
Now taking the p term common from the first bracket
\[ \Rightarrow p\left( {pq - {r^2}} \right) - \left( {pq - {r^2}} \right)\]
In the above equation obtained, we can take \[pq - {r^2}\] term common
\[ \Rightarrow \left( {pq - {r^2}} \right)\left( {p - 1} \right)\]
The above equation obtained is the factored form of the given equation. When we multiply the factorize equation, we will obtain the same equation given above.

Additional Information- The word polynomial is derived from the word poly means many and the word nominal means term so the word polynomial means many terms. It is made up of the terms which can be added, subtracted or multiplied. The highest exponent of the variable in the polynomial is called its degree and depending upon the degree of the polynomials, they are named as linear whose degree is one, quadratic with degree two and cubic with degree three and so on.

Note- In order to solve these types of questions, we need to learn about the polynomial equation and the formula of the algebraic equation. With the help of factorization method we reduce any algebraic or quadratic equation into simpler form, so that the equation can be represented into the product of factors instead of expanding the brackets.