Question

select the correct answer.

which expression is equivalent to this polynomial expression?

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

\\(\bigcirc 3x^2y^2 + 6xy^2 + 6x^2 + 3\\)
\\(\bigcirc 3x^2y^2 + 4xy^2 + 3x^2 + 3y^2 - 3\\)
\\(\bigcirc 8x^2y^2 + 2xy^2 - 4y^2 + 4\\)
\\(\bigcirc 9x^2y^2 + 4xy^2 - 3\\)

Explanation:

Group like terms

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

Combine coefficients

$$ 3x^2y^2 + (5 - 1)xy^2 + 3x^2 + 3y^2 + (-3) $$

Simplify the expression

$$ 3x^2y^2 + 4xy^2 + 3x^2 + 3y^2 - 3 $$

Answer:

• (A) \(3x^2y^2 + 6xy^2 + 6x^2 + 3\)
• (B) \(3x^2y^2 + 4xy^2 + 3x^2 + 3y^2 - 3\) (Correct answer)
• (C) \(8x^2y^2 + 2xy^2 - 4y^2 + 4\)
• (D) \(9x^2y^2 + 4xy^2 - 3\)