Question

Which expression is equivalent to the polynomial expression:

(5xy^2 + 3x^2 - 7) + (3x^2y^2 - xy^2 + 3y^2 + 4)?

A) 8x^2y^2 + 3x^2 + 3y^2 - 3.
B) 8x^2y^2 + 6x^2 - 2xy^2 + 4y^2 - 3.
C) 8x^2y^2 + 6x^2 - 2xy^2 + 4y^2 + 1.
D) 5x^2y^2 + 6x^2 - 6xy^2 + 7y^2 - 3.

Answer 1

To find the equivalent expression, combine like terms of the given polynomial by adding coefficients of terms with the same variable factors. This results in the expression 8x^2y^2 + 3x^2 + 3y^2 - 3, which corresponds to option (A).

Step-by-step explanation:

The question asks which expression is equivalent to the polynomial expression (5xy^2 + 3x^2 - 7) + (3x^2y^2 - xy^2 + 3y^2 + 4).

We need to combine like terms, which means we must add coefficients of the terms that have the same variables raised to the same powers. By doing this, we get:

1. Combine 5xy^2 and -xy^2: (5 - 1)xy^2 = 4xy^2.
2. Combine 3x^2 and 3x^2y^2: These cannot be combined as they are not like terms.
3. Combine the constants -7 and +4: -7 + 4 = -3.
4. Now we rewrite the expression with combined like terms: (3x^2y^2 + 4xy^2 + 3x^2 + 3y^2 - 3).

Therefore, the equivalent expression is option (A) 8x^2y^2 + 3x^2 + 3y^2 - 3.