A) \[(2x+z)(2{{x}^{3}}+{{z}^{3}}-2{{x}^{2}})\]
B) \[z(x+2z)({{x}^{2}}+{{z}^{2}}-{{x}^{2}})\]
C) \[z(2x-z)(2{{x}^{2}}-2xz+{{z}^{2}})\]
D) \[z(x-2z)(2{{z}^{2}}-2xz+{{x}^{2}})\]
Correct Answer: C
Solution :
\[{{x}^{4}}-{{(x-z)}^{4}}={{({{x}^{2}})}^{2}}-{{[{{(x-z)}^{2}}]}^{2}}\] \[=[{{x}^{2}}+{{(x-z)}^{2}}][{{x}^{2}}-{{(x-z)}^{2}}]\] \[=[{{x}^{2}}+{{(x-z)}^{2}}][\{x+(x-z)\}\{x-(x-z)\}]\] \[=[{{x}^{2}}+{{(x-z)}^{2}}][(2x-z)(z)]\] \[=(2x-z)z(2{{x}^{2}}+{{z}^{2}}-2xz)\]
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