Which one of the following is a factor of 3\sqrt{3}x^{3}+2\sqrt{2}y^{3}-18xy+6\sqrt{6}?
- A. \sqrt{3}x+\sqrt{2}y-\sqrt{3}
- B. \sqrt{3}x+\sqrt{2}y-\sqrt{6}
- C. 3x^{2}+2y^{2}-\sqrt{18}x-\sqrt{12}y-\sqrt{6}xy+6 ✓
- D. 3x^{2}+2y^{2}+\sqrt{18}x+\sqrt{12}y-\sqrt{6}xy+6
Correct Answer: C. 3x^{2}+2y^{2}-\sqrt{18}x-\sqrt{12}y-\sqrt{6}xy+6
Explanation
The expression fits the identity A^3+B^3+C^3-3ABC with A=\sqrt{3}x, B=\sqrt{2}y, C=\sqrt{6}. This factors into (A+B+C)(A^2+B^2+C^2-AB-BC-CA). Substituting the values into the second factor gives 3x^2+2y^2+6-\sqrt{6}xy-\sqrt{12}y-\sqrt{18}x.
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