Question

How do you combine like terms in \[4{{p}^{4}}+7{{p}^{2}}-3{{p}^{3}}-8-3{{p}^{2}}-2{{p}^{4}}-8-3{{p}^{2}}-2{{p}^{4}}\]?

Answer 1

Hint: From the question we have been asked to combine the like terms in \[4{{p}^{4}}+7{{p}^{2}}-3{{p}^{3}}-8-3{{p}^{2}}-2{{p}^{4}}-8-3{{p}^{2}}-2{{p}^{4}}\]. For this question we are given algebraic terms that have the variable \[p\], but the degree of the terms are different. So, we will find the terms which are having the same degree. By finding next we will add the terms of the same degree and simplify them. In this way we will solve the questions.

Complete step by step solution:
Firstly, as mentioned above we will find the terms of the same degree and rearrange them and we will use the addition operation and add them. So, the equation after finding terms of the same degree and combining them will be as follows.
\[\Rightarrow 4{{p}^{4}}+7{{p}^{2}}-3{{p}^{3}}-8-3{{p}^{2}}-2{{p}^{4}}-8-3{{p}^{2}}-2{{p}^{4}}\]
Here we have three terms with the power 4 so after bringing them together we get the equation reduced as follows.
\[\Rightarrow \left( 4{{p}^{4}}-2{{p}^{4}}-2{{p}^{4}} \right)+7{{p}^{2}}-3{{p}^{3}}-8-3{{p}^{2}}-8-3{{p}^{2}}\]
Now, we will combine the terms which are having the degree 2. So, the expression will be reduced as follows.
\[\Rightarrow \left( 4{{p}^{4}}-2{{p}^{4}}-2{{p}^{4}} \right)+\left( 7{{p}^{2}}-3{{p}^{2}}-3{{p}^{2}} \right)-8-3{{p}^{3}}-8\]
Now, we combine the constant terms. So the expression will be reduced as follows.
\[\Rightarrow \left( 4{{p}^{4}}-2{{p}^{4}}-2{{p}^{4}} \right)+\left( 7{{p}^{2}}-3{{p}^{2}}-3{{p}^{2}} \right)+\left( -8-8 \right)-3{{p}^{3}}\]
So, now we will use the basic operation which is addition and add the coefficients of the terms having equal degree. So, the expression will be simplified as follows.
\[\Rightarrow \left( 4{{p}^{4}}-2{{p}^{4}}-2{{p}^{4}} \right)+\left( 7{{p}^{2}}-3{{p}^{2}}-3{{p}^{2}} \right)+\left( -8-8 \right)-3{{p}^{3}}\]
\[\Rightarrow \left( 0{{p}^{4}} \right)+\left( {{p}^{2}} \right)-16-3{{p}^{3}}\]
\[\Rightarrow -3{{p}^{3}}+{{p}^{2}}-16\]
Therefore, in this way we combine the like terms and the resultant will be \[ -3{{p}^{3}}+{{p}^{2}}-16\].

Note: Students must be very careful in doing the calculations. Students should perform the basic operation that is addition without any mistake. Here we get confusion as there are many terms so we must be careful in doing this question. Here we should add only like terms in these questions we should not do mistakes like adding the unlike terms each other for example in this expression \[\Rightarrow 4{{p}^{4}}+7{{p}^{2}}-3{{p}^{3}}-8-3{{p}^{2}}-2{{p}^{4}}-8-3{{p}^{2}}-2{{p}^{4}}\] we should not add \[-3{{p}^{3}}\]and \[-3{{p}^{2}}\] which makes our solution a wrong. So, we must be careful and patience in checking the degree of terms..