Question

How do you find the sum or difference of \[(3{n^3} + {n^2} - 5n) - ( - 8{n^2} - 3{n^3})\]?

Answer 1

Hint: Here in this question we have to solve the expression by solving the bracket and then solving the terms together whose power to the variable are same, that means linear term will be solved with linear term and square term will be solved by solving with square term.

Complete step by step solution:
The given question is \[(3{n^3} + {n^2} - 5n) - ( - 8{n^2} - 3{n^3})\]
First here we have to first solving the bracket, on solving we get:
\[
   \Rightarrow (3{n^3} + {n^2} - 5n) - ( - 8{n^2} - 3{n^3}) \\
   \Rightarrow 3{n^3} + {n^2} - 5n + 8{n^2} + 3{n^3} \\
 \]
Now we have to solve for the same power variables, addition and subtraction will be done to the same power variables and similarly addition will be done to the same square terms, on solving we get:
\[
   \Rightarrow 3{n^3} + {n^2} - 5n + 8{n^2} + 3{n^3} \\
   \Rightarrow 6{n^3} + 9{n^2} - 5n \\
 \]
This is the required final solution for the question.
Here in addition we can solve for the factors of the solution, but not asked in the question so we are not solving further to get the solution for the given quadratic equation.

Note: This kind of mixed quadratic and linear term equation needed to be solved as per the instruction given in the question, here we are only asked to solve the bracket and get the final solution, so we have done that but if question doesn’t provide the instruction then we have to move till the final solution of the equation by equating the term to zero.