Question

How do you combine $\left( 4{{n}^{3}}-4{{n}^{2}}-5n \right)+\left( 6{{n}^{2}}+5{{n}^{3}}-7n \right)$ ?

Answer 1

Hint: Here in this question we have been asked to simplify the given algebraic expression $\left( 4{{n}^{3}}-4{{n}^{2}}-5n \right)+\left( 6{{n}^{2}}+5{{n}^{3}}-7n \right)$ . For answering this question we will perform simple basic arithmetic operations between the similar terms in the given algebraic expression.

Complete step-by-step answer:
Now considering from the question we have been asked to simplify the given algebraic expression $\left( 4{{n}^{3}}-4{{n}^{2}}-5n \right)+\left( 6{{n}^{2}}+5{{n}^{3}}-7n \right)$ .
For answering this question we will perform simple basic arithmetic operations between the similar terms in the given algebraic expression.
Firstly let us remove the brackets in the given expression. After doing that we will have $\Rightarrow 4{{n}^{3}}-4{{n}^{2}}-5n+6{{n}^{2}}+5{{n}^{3}}-7n$ .
Now we will perform simple basic arithmetic addition between the terms containing ${{n}^{3}}$ . After doing that we will have $\Rightarrow 9{{n}^{3}}-4{{n}^{2}}-5n+6{{n}^{2}}-7n$ .
Now we will perform simple basic arithmetic addition between the terms containing ${{n}^{2}}$ . After doing that we will have $\Rightarrow 9{{n}^{3}}+2{{n}^{2}}-5n-7n$ .
Now we will perform simple basic arithmetic addition between the terms containing $n$ . After doing that we will have $\Rightarrow 9{{n}^{3}}+2{{n}^{2}}-12n$ .
Therefore we can conclude that the simplified form of the given algebraic expression $\left( 4{{n}^{3}}-4{{n}^{2}}-5n \right)+\left( 6{{n}^{2}}+5{{n}^{3}}-7n \right)$ will be given as $9{{n}^{3}}+2{{n}^{2}}-12n$ .

Note: While answering questions of this type we should be sure with the calculations that we are going to perform in between the steps for simplifying the given algebraic expression. This is a very simple and easy question and can be answered accurately in a short span of time. Very few mistakes are possible in questions of this type. Someone can make a mistake and consider it as
$\begin{align}
  & \left( 4{{n}^{3}}-4{{n}^{2}}-5n \right)+\left( 6{{n}^{2}}+5{{n}^{3}}-7n \right) \\
 & \Rightarrow 4{{n}^{3}}-4{{n}^{2}}-5n+6{{n}^{2}}+5{{n}^{3}}-7n \\
 & \Rightarrow 9{{n}^{3}}-2{{n}^{2}}-5n \\
\end{align}$
which will lead them to end up having a wrong answer.