Question

Simplify the expressions. Show work.
(5x^4 - 3x^3 + 6x)-(3x^3 + 11x^2 -8x)

I know there are two ways to do this but I am trying one way and having a problem with one part.
So far I have

5x^4 - 3x^3 + 6x - 3x^3 + 11x^2 - 8x
(5x^4 - 3x^3) + (3x^3 - 11x^2) + 6x + 8x


From here not so sure assuming I have it right so far that is. Does the (5x^4 - 3x^3) become 2x with no ^# or do I subtract them as well that makes 2x^1 which would still be 2x.

Answer 1

You can only subtract like powers.
So, 5x^4 - 3x^4 = (5-3)x^4 = 2x^4

Answer 2

But you can't subtract 5x^4-3x^3.

Answer 3

i.e. 5x^4 - 3x^3 is as simple as it could get.

Answer 4

5x^4 - 3x^3 + 6x - 3x^3 + 11x^2 - 8x there are sign problem here

Answer 5

So it doesn't change then? It stays 5x^4 - 3x^3? So I have it completely wrong?

Answer 6

5x^4 - 3x^3 + 6x - 3x^3 -* 11x^2+ 8x

Answer 7

5x^4 - 3x^3 + 6x - 3x^3 - 11x^2 + 8x

Answer 8

You want to reorder the terms. So that all the x^4's are grouped,
x^3's are grouped, etc. Place parentheses around like terms

Answer 9

(5x^4 - 3x^3 + 6x)-(3x^3 + 11x^2 -8x) --> 5x^4 + ( - 3x^3 - 3x^3 ) -11x^2+ (6x + 8x)

Answer 10

Then, factor out the x's from each set of parentheses -- like this:
5x^4 + ( - 3 - 3 )x^3 -11x^2+ (6 + 8)x

Answer 11

Could you do it on a test? Knowing that?

Answer 12

So, 5x^4 + ( - 3x^3 - 3x^3 ) -11x^2+ (6x + 8x)
5x^4 + 11x^2+ 14x ?

Answer 13

almost, but the x^3 terms don't cancel because they're both negative.

Answer 14

Instead, they combine to make -6x^3.

Answer 15

Does the + become - then like this?
5x^4 - 6x^3 + 11x^2+ 14x

Answer 16

Yep.

Answer 17

Great. Thanks so much for helping. Helped a lot.

Answer 18

Yw (: