What is the HCF of (x^{8}-y^{8}) and (x^{7}-y^{7}+x^{5}y^{2}-x^{2}y^{5})?
- A. (x^{2}+y^{2})
- B. (x^{2}-y^{2})
- C. (x^{3}-y^{3}-x^{2}y+xy^{2}) ✓
- D. (x^{3}-y^{3}+x^{2}y-xy^{2})
Correct Answer: C. (x^{3}-y^{3}-x^{2}y+xy^{2})
Explanation
(x^8-y^8) = (x^4-y^4)(x^4+y^4) = (x-y)(x+y)(x^2+y^2)(x^4+y^4). The second expression factors as x^5(x^2+y^2)-y^5(x^2+y^2) = (x^5-y^5)(x^2+y^2) = (x-y)(x^4+x^3y+...)(x^2+y^2). Their HCF is (x-y)(x^2+y^2) = x^3-x^2y+xy^2-y^3.
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