Question

How do you simplify $\left( 5{{x}^{4}}-3{{x}^{3}}+6x \right)-\left( 3{{x}^{3}}+11{{x}^{2}}-8x \right)$?

Answer 1

Hint: To solve the given expression first we will multiply by the minus sign to the terms given in the second bracket. Then we will add or subtract the terms with the same variable power. Then by simplifying the obtained equation we get the desired answer.

Complete step by step solution:
We have been given that $\left( 5{{x}^{4}}-3{{x}^{3}}+6x \right)-\left( 3{{x}^{3}}+11{{x}^{2}}-8x \right)$.
We have to simplify the given expression.
We know that to solve the given expression first we have to solve the brackets. Now, let us first multiply the second bracket by minus sign and open the bracket. Then we will get
$\Rightarrow \left( 5{{x}^{4}}-3{{x}^{3}}+6x \right)-3{{x}^{3}}-11{{x}^{2}}+8x$
Now, opening the first bracket we will get
$\Rightarrow 5{{x}^{4}}-3{{x}^{3}}+6x-3{{x}^{3}}-11{{x}^{2}}+8x$
Now, simplifying the above obtained equation we will get
$\Rightarrow 5{{x}^{4}}-6{{x}^{3}}-11{{x}^{2}}+14x$
Hence above is the required simplified form of the given expression.

Note: The possibility of mistake while solving the given expression is that students directly solve the brackets without multiplying the terms by minus sign. Then we will get the solution as
$\Rightarrow 5{{x}^{4}}-3{{x}^{3}}+6x-3{{x}^{3}}+11{{x}^{2}}-8x$
Now, simplifying the above obtained equation we will get
$\Rightarrow 5{{x}^{4}}-6{{x}^{3}}+11{{x}^{2}}-2x$ which is the incorrect solution. So while adding or multiplying combinations of positive and negative numbers students must be careful. When we have to multiply two minus signs it becomes plus, one minus sign and one plus sign becomes one minus sign, two plus sign becomes plus.