Question

(Adding and Subtracting Polynomials)

Answer 1

Adding and subtracting big polynomials like these are pretty easy. You just need to combine like terms. For example:

1.)

${5x}^{2} + {3x}^{2} = {8x}^{2}$

2.)

$({3x}^{2} + 5xy) + (7xy + 2) =$

${3x}^{2} + 12xy + 2$

(The 3x^2 and the 2 stay intact while the 5xy and 7xy combine together)

All you have to do is combine the numbers that have the same powers of x and y with each other. x^2 will combine with x^2 and xy^2 wil combine with xy^2 exc. If there is no other number with the same x and y's, then you just leave it as it is in the answer.

Now with the original question, I see a -9xy^3, and thats gonna combine with the 3xy^3 in the second polynomial and the 2xy^3 in the third one.

$- 9x {y}^{3} + 3x {y}^{3} + 2x {y}^{3} = \\ - 4x {y}^{3}$

So far we have -4xy^3, the next term is going to be a -9x^4y^3, and that's gonna combine with the 3x^4y^3 in the third one.

$- 9 {x}^{4} {y}^{3} + 3 {x}^{4} {y}^{3} = - 6{x}^{4} {y}^{3}$

We now finished adding the like terms that were in the first polynomial, we will move onto the second polynomial. The first term in this one is 3xy^3, in which we already added in the first step. At this point, it doesn't look like there are any other terms that have the same x and y behind them. So we can move on and write the final answer:

$- 4x {y}^{3} - 6 {x}^{4} {y}^{3} + 7 {y}^{4} \\ - 8 {x}^{4} {y}^{4}$

(All on the same line of course)

Also, for your second question, the order does not matter in which you write the terms. I could write the 7y^4 behind the -8x^4y^4 and it would still be the same answer.

If you have any other questions let me know :) while I double check my work.