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\\) a. $3x^2y^2 + 6xy^2 + 6x^2 + 3$
\\(\bigcirc\\) b. $8x^2y^2 + 2xy^2 - 4y^2 + 4$
\\(\bigcirc\\) c. $9x^2y^2 + 4xy^2 - 3$
\\(\bigcirc\\) d. $3x^2y^2 + 4xy^2 + 3x^2 + 3y^2 - 3$

Explanation:

Step1: Remove parentheses

We have \((5xy^{2}+3x^{2}-7)+(3x^{2}y^{2}-xy^{2}+3y^{2}+4)\). Removing the parentheses gives \(5xy^{2}+3x^{2}-7 + 3x^{2}y^{2}-xy^{2}+3y^{2}+4\).

Step2: Combine like terms

• For \(xy^{2}\) terms: \(5xy^{2}-xy^{2}=4xy^{2}\)
• For constant terms: \(-7 + 4=-3\)
• The other terms \(3x^{2}\), \(3x^{2}y^{2}\), and \(3y^{2}\) remain as they are.

Combining all these, we get \(3x^{2}y^{2}+4xy^{2}+3x^{2}+3y^{2}-3\).

Answer:

D. \(3x^{2}y^{2}+4xy^{2}+3x^{2}+3y^{2}-3\)