Question

How do you find the sum or difference of $\left( 6{{x}^{3}}-4 \right)+\left( -2{{x}^{3}}+9 \right)?$

Answer 1

Hint: We will use the concept of algebraic polynomial to solve the above question. To solve the above given polynomial, we will first remove all the parenthesis by taking special care of the sign and then we will simplify similar terms together by taking the variable common and simplifying the constant.

Complete step-by-step solution:
We can see that the above question is of algebra polynomial so we will use the concept of simplification of algebraic polynomials to solve the above question.
We will first remove all the parenthesis by taking special care of the sign as when we have minus sign outside a bracket then while removing that bracket, we are required to invert the sign of all the terms inside of that bracket.
Since, from question we have expression $\left( 6{{x}^{3}}-4 \right)+\left( -2{{x}^{3}}+9 \right)$ and we have to simplify it:
So, at first after removing all the brackets we will get:
$\Rightarrow 6{{x}^{3}}-4-2{{x}^{3}}+9$
Now, we will group all the similar terms together.
\[\Rightarrow 6{{x}^{3}}-2{{x}^{3}}-4+9\]
Now, we will take ${{x}^{3}}$ common from the first two terms of the above expression, then we will get:
\[\Rightarrow \left( 6-2 \right){{x}^{3}}-4+9\]
Now, after simplifying we will get:
\[\Rightarrow \left( 4 \right){{x}^{3}}+5\]
\[\Rightarrow 4{{x}^{3}}+5\]
Now, we can see that we cannot simplify the above expression further.
So, $\left( 6{{x}^{3}}-4 \right)+\left( -2{{x}^{3}}+9 \right)$ = \[4{{x}^{3}}+5\].
This is our required answer.

Note: In this type of question students are only required to take special care while removing the bracket as there is change in sign of terms inside the bracket when we have negative signs outside the bracket. Also, students should avoid any calculation mistake.