A) \[{{(4x-3y)}^{3}}\]
B) \[{{(16{{x}^{2}}+12xy+9{{y}^{2}})}^{2}}\]
C) \[64{{x}^{3}}-27{{y}^{3}}\]
D) \[64{{x}^{3}}+27{{y}^{3}}\]
Correct Answer: C
Solution :
\[(4x-3y)\,(16{{x}^{2}}+12xy+9{{y}^{2}})\] \[=(4x-3y)\,(16{{x}^{2}}+12xy+9{{y}^{2}})\] \[=(4x)\,(16{{x}^{2}}+12xy+9{{y}^{2}})\] \[+(-3y)\,(16{{x}^{2}}+12xy+9{{y}^{2}})\] \[=64{{x}^{3}}+48{{x}^{2}}y+36x{{y}^{2}}\] \[-48{{x}^{2}}y-36x{{y}^{2}}-27{{y}^{3}}\] \[=64{{x}^{3}}-27{{y}^{3}}\]
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