Question

How do you subtract $2{{x}^{2}}-6x-4$ from $4{{x}^{2}}-4x+3$?

Answer 1

Hint: We will see the definition of subtraction. Then we will see how subtraction works for polynomials. We will look at an example to understand the subtraction for polynomials. Then we will use this concept to perform subtraction on the given polynomials. Then we will obtain the result as a polynomial, which will be the difference between the given polynomials.

Complete step by step answer:
Subtraction is an arithmetic operation which is performed on a collection of objects by removing a certain number of objects from another number of objects. For subtracting one polynomial from the other, we first reverse the signs of the terms in the polynomial that is to be subtracted. Then we rearrange the terms so that the terms with the same variable are grouped together. After that we will do the arithmetic operations in the expression on the coefficients of the similar terms.
We will use the above method to do the subtraction for the given polynomials. We have to subtract $2{{x}^{2}}-6x-4$ from $4{{x}^{2}}-4x+3$. The expression looks like the following,
$4{{x}^{2}}-4x+3-\left( 2{{x}^{2}}-6x-4 \right)$
Now, we will reverse the signs of the terms in the polynomial to be subtracted, which is $2{{x}^{2}}-6x-4$. So, we obtain $-2{{x}^{2}}+6x+4$. So, the expression becomes,
$4{{x}^{2}}-4x+3-2{{x}^{2}}+6x+4$
Next, we will rearrange the terms so that similar terms are grouped together. The expression becomes the following,
\[4{{x}^{2}}-2{{x}^{2}}-4x+6x+3+4\]
Performing the arithmetic operations in the above expression, we get the following,
\[2{{x}^{2}}+2x+7\]
Therefore, we get $4{{x}^{2}}-4x+3-\left( 2{{x}^{2}}-6x-4 \right)=2{{x}^{2}}+2x+7$.

Note:
We should be familiar with all the arithmetic operations and their definitions. It is important to understand how these operations work on polynomials. Addition or subtraction of a polynomial from another polynomial will give the same degree of polynomial in the result, unless the highest degree term coefficients get cancelled with each other.