ANSWER
The correct answer is B
EXPLANATION
The given sum is
[tex] \sqrt{ {x}^{2} {y}^{3} } + 2 \sqrt{ {x}^{3} {y}^{4} } + xy \sqrt{y} [/tex]
We need to remove the perfect squares.
[tex]\sqrt{ {x}^{2} \times {y}^{2} \times y } + 2 \sqrt{ {x}^{2} \times ( {y}^{2})^{2} \times x } + xy \sqrt{y} [/tex]
Let us split the radical sign for the factors to get;
[tex]\sqrt{ {x}^{2}} \times \sqrt{ {y}^{2}} \times \sqrt{y} + 2 \sqrt{ {x}^{2} } \times \sqrt{( {y}^{2})^{2}} \times \sqrt{x} + xy \sqrt{y} [/tex]
This simplifies to
[tex]xy \sqrt{y} + 2x {y}^{2} \sqrt{x} + xy \sqrt{y} [/tex]
Group similar terms to get:
[tex]xy\sqrt{y} + xy \sqrt{y} + 2x {y}^{2} \sqrt{x} [/tex]
Combine the similar terms to get:
[tex]2xy\sqrt{y} + 2x {y}^{2} \sqrt{x} [/tex]
The correct answer is B.
