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Coordinate Geometry

Question
CBSEENMA9001843

Simplify:

open parentheses straight x minus 2 over 3 straight y close parentheses cubed minus open parentheses x plus 2 over 3 y close parentheses cubed

Solution
open parentheses straight x minus 2 over 3 straight y close parentheses cubed minus open parentheses straight x plus 2 over 3 straight y close parentheses cubed
equals space open square brackets straight x cubed minus open parentheses 2 over 3 straight y close parentheses cubed minus 3 left parenthesis straight x right parenthesis open parentheses 2 over 3 straight y close parentheses open curly brackets open parentheses straight x close parentheses minus open parentheses 2 over 3 straight y close parentheses close curly brackets close square brackets
equals space open square brackets straight x cubed minus open parentheses 2 over 3 straight y close parentheses cubed plus 3 left parenthesis straight x right parenthesis open parentheses 2 over 3 straight y close parentheses open curly brackets open parentheses straight x close parentheses plus open parentheses 2 over 3 straight y close parentheses close curly brackets close square brackets
equals open square brackets straight x cubed minus 8 over 27 straight y cubed minus 2 straight x squared straight y plus 4 over 3 xy squared close square brackets minus open square brackets straight x cubed plus 8 over 27 straight y cubed plus 2 straight x squared straight y plus 4 over 3 xy squared close square brackets
equals space minus 16 over 27 straight y cubed minus 4 straight x squared straight y