Expand : ( a+b+c)³.
Answers
Answer:
(a+b+c)³=(a³+3a²b+3ab²+b³)+3(a²+2ab+b²)c+3(a+b)c2+c³
(a+b+c)³=a³+b³+c³+3a²b+3a²c+3ab²+3b²c+3ac²+3bc²+6abc
(a+b+c)³=(a³+b³+c³)+(3a²b+3a²c+3abc)+(3ab²+3b²c+3abc)+(3ac²+3bc²+3abc)−3abc
(a+b+c)³=(a³+b³+c³)+3a(ab+ac+bc)+3b(ab+bc+ac)+3c(ac+bc+ab)−3abc
(a+b+c)³=(a³+b³+c³)+3(a+b+c)(ab+ac+bc)−3abc
(a+b+c)³=(a³+b³+c³)+3[(a+b+c)(ab+ac+bc)−abc]
Answer:
a³ + b³ + c³ + 3a²b + 3ab² + 3b²c + 3bc² + 3a²c + 3ac² + 6abc
Step-by-step explanation:
( a + b + c )³
= ( a + b + c )( a + b + c )( a + b + c )
= ( a² + ab + ac + ab + b² + bc + ac + bc + c² )( a + b + c )
[Multiplied two first two terms]
= ( a² + b² + c² + 2ab + 2bc + 2ac )( a + b + c )
= a³ + ab² + ac² + 2a²b + 2abc + 2a²c + a²b + b³ + bc² + 2ab² + 2b²c + 2abc + a²c + b²c + c³ + 2abc + 2bc² + 2ac²
[Multiplied rest two terms]
= a³ + b³ + c³ + 3a²b + 3ab² + 3b²c + 3bc² + 3a²c + 3ac² + 6abc
Ans:- a³ + b³ + c³ + 3a²b + 3ab² + 3b²c + 3bc² + 3a²c + 3ac² + 6abc
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