Question

What is the difference of the polynomials (x^4+x^3+x^2+x)-(x^4-x3+x^2-x)

Answer 1

Hello!

The answer is:

The difference of the given polynomials is:

`2x^(3)+2x`

Why?

To solve this problem we need to group like terms and then add or subtract them. We must remember that like terms are terms that have equal coefficient and equal exponents.

For example,

`x+x=x^(2)`

Both "x" are like terms because they have the same coefficient and the same exponent, se we could add them.

So, from the problem we have:

`(x^(4)+x^(3)+x^(2)+x)-(x^(4)-x^(3)+x^(2)-x)=(x^(4)+x^(3)+x^(2)+x)-x^(4)+x^(3)-x^(2)+x\\\\x^(4)+x^(3)+x^(2)+x-x^(4)+x^(3)-x^(2)+x=x^(4)-x^(4)+x^(3)+x^(3)+x^(2)-x^(2) +x+x\\\\x^(4)-x^(4)+x^(3)+x^(3)+x^(2)-x^(2) +x+x=0+2x^(3)-0+2x`

So, the answer will be:

`(x^(4)+x^(3)+x^(2)+x)-(x^(4)-x^(3)+x^(2)-x)=2x^(3)+2x`

Have a nice day!

Answer 2

Answer:
`2x^3+2x`

Explanation:

The difference is obtained by subtracting the polynomial
`(x^4+x^3+x^2+x)` and the polynomial
`(x^4-x3+x^2-x)`.

It is important to remember the multiplication of signs:

`(-)(-)=+\\(+)(+)=+\\(-)(+)=-`

Then, you can subtract both polynomials to find the difference.

You need to Distribute the negative sign:

`(x^4+x^3+x^2+x)-(x^4-x3+x^2-x)=x^4+x^3+x^2+x-x^4+x3-x^2+x`

Finally, you have to add the like terms. Then:

`=2x^3+2x`