Question

Enter your answer. in standard form, in the box.​

Answer 1

`=-5x^5-5x^4+6x^3-x^2-7x+20`

OR

`=-5x^5-5x^4+6x^3-x^2-7x^1+20x^0`

The above two is written in standard form:

Explanation:

Step 1: Remove the parenthesis:

`(2x^(5)+x^(3)-3x^(4)-x+8)-(7x^(5)+2x^(4)-12+6x-5x^(3)+x^(2))`

`=2x^5+x^3-3x^4-x+8-\left(7x^5+2x^4-12+6x-5x^3+x^2\right)`

Step 2: Focus on the equation with the parenthesis:

`-\left(7x^5+2x^4-12+6x-5x^3+x^2\right)`

Step 3 and 4: Distribute the parenthesis and apply rules

`-\left(-a\right)=a,\:\:\:-\left(a\right)=-a`

`=-\left(7x^5\right)-\left(2x^4\right)-\left(-12\right)-\left(6x\right)-\left(-5x^3\right)-\left(x^2\right)`

`=-7x^5-2x^4+12-6x+5x^3-x^2`

Step 5: Now look at the whole thing:

`2x^5+x^3-3x^4-x+8-7x^5-2x^4+12-6x+5x^3-x^2`

Step 6: Move all the terms with variables to the right and constants to the right, group like terms:

`=2x^5-7x^5-3x^4-2x^4+x^3+5x^3-x^2-x-6x+8+12`

Step 7: Add similar elements or terms :
`x^3+5x^3=6x^3`:

`=2x^5-7x^5-3x^4-2x^4+6x^3-x^2-x-6x+8+12`

Step 8: Add similar elements or terms :
`-3x^4-2x^4=-5x^4`

`=2x^5-7x^5-5x^4+6x^3-x^2-x-6x+8+12`

Step 9: Add similar elements or terms:
`2x^5-7x^5=-5x^5`

`=-5x^5-5x^4+6x^3-x^2-x-6x+8+12`

Step 10: Add similar elements or terms:
`-x-6x=-7x`

`=-5x^5-5x^4+6x^3-x^2-7x+8+12`

Step 11: Add similar elements or terms:
`8+12=20`

`=-5x^5-5x^4+6x^3-x^2-7x+20`

Step 12 : ANSWER:

`=-5x^5-5x^4+6x^3-x^2-7x+20`

The standard from can be written as :

`=-5x^5-5x^4+6x^3-x^2-7x+20`

`=-5x^5-5x^4+6x^3-x^2-7x^1+20x^0`

Why
`x^0` and
`x^1`?

If x equals 2...

Same results

That is how you order constants in standard form. Always add a constant to the 0 power with a variable to make you have a better understanding.

`20=20\\20x^0=20(2)^0=20(1)=20`

`-7x=-7(2)=-14\\-7x^1=-7(2)^1=-7(2)=-14`