Home » Past Questions » Math » \( (x^2y - 3y^2 + 5xy^2) - (-x^2y + 3xy^2 - 3y^2) \)Which of the following is eq...

\( (x^2y - 3y^2 + 5xy^2) - (-x^2y + 3xy^2 - 3y^2) \)Which of the following is eq...

Question

\( (x^2y - 3y^2 + 5xy^2) - (-x^2y + 3xy^2 - 3y^2) \)

Which of the following is equivalent to the expression above?

Options

\( 4x^2y^2 \)

\( 8xy^2 - 6y^2 \)

\( 2x^2y + 2xy^2 \)

\( 2x^2y + 8xy^2 - 6y^2 \)

The correct answer is C.

Explanation:

Choice C is correct. Only like terms, with the same variables and exponents, can be combined to determine the answer as shown here:
\( (x^2y - 3y^2 + 5xy^2) - (-x^2y + 3xy^2 - 3y^2) \)
\( = (x^2y - (-x^2y)) + (-3y^2 - (-3y^2)) + (5xy^2 - 3xy^2) \)
\( = 2x^2y + 0 + 2xy^2 \)
\( = 2x^2y + 2xy^2 \)
Choices A, B, and D are incorrect and are the result of common calculation errors or of incorrectly combining like and unlike terms.