What is the answer of(A+B+C)3
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Posted by Shiv Pawadashetti 5 years, 3 months ago
- 2 answers
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Sia ? 5 years, 3 months ago
{tex}( a + b + c ) ^ { 3 } = [ a + ( b + c ) ] ^ { 3 }{/tex}
{tex}= a ^ { 3 } + 3 a ^ { 2 } ( b + c ) + 3 a ( b + c ) ^ { 2 } + ( b + c ) ^ { 3 }{/tex}
{tex}= a ^ { 3 } + 3 a ^ { 2 } b + 3 a ^ { 2 } c + 3 a[ \left( b ^ { 2 } + 2 b c + c ^ { 2 } \right)] + \left( b ^ { 3 } + 3 b ^ { 2 } c + 3 b c ^ { 2 } + c ^ { 3 } \right){/tex}
{tex}= a ^ { 3 } + 3 a ^ { 2 } b + 3 a ^ { 2 } c + 3 a b ^ { 2 } + 6 a b c + 3 a c ^ { 2 } + b ^ { 3 } + 3 b ^ { 2 } c + 3 b c ^ { 2 } + c ^ { 3 }{/tex}
{tex}= a ^ { 3 } + b ^ { 3 } + c ^ { 3 } + 3 a ^ { 2 } b + 3 a ^ { 2 } c + 3 b ^ { 2 } c + 3 b ^ { 2 } a + 3 c ^ { 2 } a + 3 c ^ { 2 } b + 6 a b c{/tex}
{tex}= a ^ { 3 } + b ^ { 3 } + c ^ { 3 } + 3 a ^ { 2 } ( b + c ) + = a ^ { 3 } + b ^ { 3 } + c ^ { 3 } + 3 a ^ { 2 } ( b + c ){/tex}
{tex}\therefore{/tex}{tex}( a + b + c ) ^ { 3 } = a ^ { 3 } + b ^ { 3 } + c ^ { 3 } + 3 ( a + b ) ( b + c ) ( c + a ){/tex}
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