What is the LCM of x^{4}+x^{2}y^{2}+y^{4}, x^{3}+y^{3}, x^{3}-y^{3}?
- A. (x^{2}-y^{2})(x^{4}+x^{2}y^{2}+y^{4})^{2}
- B. (x^{2}-y^{2})(x^{4}+2x^{2}y^{2}+y^{4})
- C. (x^{6}-y^{6}) ✓
- D. (x^{6}+y^{6})
Correct Answer: C. (x^{6}-y^{6})
Explanation
Factorizing: x^4+x^2y^2+y^4 = (x^2+xy+y^2)(x^2-xy+y^2); x^3+y^3 = (x+y)(x^2-xy+y^2); x^3-y^3 = (x-y)(x^2+xy+y^2). The LCM is the product of all unique factors: (x-y)(x+y)(x^2-xy+y^2)(x^2+xy+y^2) = (x^3-y^3)(x^3+y^3) = x^6-y^6.
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