Question 6 $$ \begin{array}{l}\text { Multiply }\left(x^{2}+3 y^{2}\right)\left(x^{2}+2 y^{2}\right) \ \text { OA. } x^{4}+5 x^{2} y^{2}+6 y^{4} \ \text { O. } 2 x^{4}+8 x^{2} y^{2}+6 y^{4} \ \text { O. } 6 x^{4}+11 x^{2} y^{2}+3 y^{4} \ \text { O. } 6 x^{4}+9 x^{2} y^{2}+3 y^{4}\end{array} $$

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UpStudy AI · Accepted Answer

To multiply $$ \left(x^{2}+3y^{2}\right) $$ and $$ \left(x^{2}+2y^{2}\right) $$:

1. Distribute each term in the first polynomial over the second:
   $$
   \left(x^{2}+3y^{2}\right)\left(x^{2}+2y^{2}\right) = x^{2}\left(x^{2}+2y^{2}\right) + 3y^{2}\left(x^{2}+2y^{2}\right)
   $$

2. Multiply each term:
   $$
   x^{2}\left(x^{2}+2y^{2}\right) = x^{4} + 2x^{2}y^{2}
   $$
   $$
   3y^{2}\left(x^{2}+2y^{2}\right) = 3x^{2}y^{2} + 6y^{4}
   $$

3. Combine like terms:
   $$
   x^{4} + 2x^{2}y^{2} + 3x^{2}y^{2} + 6y^{4} = x^{4} + 5x^{2}y^{2} + 6y^{4}
   $$

Thus, the correct answer is:
$$
x^{4}+5x^{2}y^{2}+6y^{4}
$$
The product is $$ x^{4} + 5x^{2}y^{2} + 6y^{4} $$.

Question 6

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