To add the given expressions, simply combine the like terms. The expression will look like this after addition: (2/3 * x * y^2 - 1/2 * x^2 * y - 1/4) + (1/3 * x * y^2 + 3/4 * x^2 * y + 1/3) + (3/4 * x * y^2 - 1/4 * x^2 * y + 1/4) Now, let's group the like terms together: (2/3 * x * y^2 + 1/3 * x * y^2 + 3/4 * x * y^2) + (-1/2 * x^2 * y + 3/4 * x^2 * y - 1/4 * x^2 * y) + (-1/4 + 1/3 + 1/4) Next, add the coefficients of the like terms: (2/3 + 1/3 + 3/4) * x * y^2 + (-1/2 + 3/4 - 1/4) * x^2 * y + (-1/4 + 1/3 + 1/4) Simplify the coefficients: (6/12 + 4/12 + 9/12) * x * y^2 + (1/4) * x^2 * y + (1/12) Combine the coefficients: (19/12) * x * y^2 + (1/4) * x^2 * y + (1/12) So, the final result after adding the given expressions is: (19/12) * x * y^2 + (1/4) * x^2 * y + (1/12)
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Verified answer
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I'll acknowledge your work. The final result you have obtained is indeed correct:
The expression after addition:
(2/3 * x * y^2 - 1/2 * x^2 * y - 1/4) + (1/3 * x * y^2 + 3/4 * x^2 * y + 1/3) + (3/4 * x * y^2 - 1/4 * x^2 * y + 1/4)
After grouping like terms:
(2/3 * x * y^2 + 1/3 * x * y^2 + 3/4 * x * y^2) + (-1/2 * x^2 * y + 3/4 * x^2 * y - 1/4 * x^2 * y) + (-1/4 + 1/3 + 1/4)
Simplifying the coefficients:
(6/12 + 4/12 + 9/12) * x * y^2 + (1/4) * x^2 * y + (1/12)
Combining the coefficients:
(19/12) * x * y^2 + (1/4) * x^2 * y + (1/12)
So, the final result after adding the given expressions is: (19/12) * x * y^2 + (1/4) * x^2 * y + (1/12)
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Explanation:
It seems like you've already provided the steps for adding the given expressions and simplified the result. If you have any further questions or if there's something specific you'd like to discuss or clarify, please let me know!