To solve this problem we need to follow the following steps:
- Remove the brackets from the given polynomials.
- Rearrange the terms so that all terms with similar power of the variables x and y are put together. Thus all terms with x^2, xy, or x will be put in three separate groups.
- Add the similar term. The result so obtained is the result of addition of the polynomials.
Following these steps we solve the question as follows:
(xy + 5x^2) + (xy - 3y) + xy
= xy + 5x^2 + xy - 3y + xy
= 5x^2 + xy + xy + xy - 3y
= 5x^2 + 3xy - 3y
5x^2 + 3xy - 3y
Please not that we have arranged the terms in the answer according to decreasing power of "x". This is not essential. But it helps to improve clarity of the polynomial.
When we add or subtract polynomials, we have to find the variables and exponents that match.
We'll remove the brackets:
xy + 5x^2 + xy - 3y + xy
Now, we'll verify if in the given expression there are terms that have matching variables.
We'll combine the terms that have the variables x*y:
xy + xy + xy = 3xy
We notice that the terms 5x^2 and - 3y do not have matching variables, so we'll add them to the final result.
The result of adding the polynomials is:
(xy+5x^2)+(xy-3y)+xy = 3xy + 5x^2 - 3y