Verified answer

To add the given expressions, we can simply combine like terms:

(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

Let's break it down further and combine the terms:

= (2/3 * x * y^2 + 1/3 * x * y^2 + 3/4 * x * y^2)

- (1/2 * x^2 * y + 1/4 * x^2 * y - 1/4 * x^2 * y)

+ (-1/4 + 1/3 + 1/4)

= (8/12 * x * y^2 + 4/12 * x * y^2 + 9/12 * x * y^2)

- (2/4 * x^2 * y + 1/4 * x^2 * y - 1/4 * x^2 * y)

+ (3/12 - 4/12 + 3/12)

= (21/12 * x * y^2)

- (2/4 * x^2 * y)

+ (2/12)

Simplifying further:

= (7/4 * x * y^2) - (1/2 * x^2 * y) + 1/6

Therefore, the sum of the expressions is (7/4 * x * y^2) - (1/2 * x^2 * y) + 1/6.

Answer:

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Step-by-step explanation:

Sure, I'll be happy to help you solve the given expressions. Let's simplify each expression step by step:

1) (2/3 * x * y^2) - (1/2 * x^2 * y) - (1/4)

2) (1/3 * x * y^2) + (3/4 * x^2 * y) + (1/3)

3) (3/4 * x * y^2) - (1/4 * x^2 * y) + (1/4)

Since you didn't provide any specific instructions regarding the variables (x and y) or their values, I'll simplify the expressions as much as possible without solving for specific values.

Step 1:

(2/3 * x * y^2) - (1/2 * x^2 * y) - (1/4)

Step 2:

(1/3 * x * y^2) + (3/4 * x^2 * y) + (1/3)

Step 3:

(3/4 * x * y^2) - (1/4 * x^2 * y) + (1/4)

These are the simplified expressions. If you have any specific questions or need further assistance with these expressions, feel free to ask. Good luck with your test!