A cube plus b cube is equal to what

Asked by admin @ 20/08/2021 in Math viewed by 280 People

Verify that a cube plus b cube equal to a + b whole into a square minus a b + b square

Answered by admin @ 20/08/2021

$\text{[math]}$ Answer :

$to \: prove = > {a}^{3} + {b}^{3} = (a + b)( {a}^{2} + {b}^{2} - ab) \\ \\ = > {a}^{3} + {b}^{ 3} = a( {a}^{2} + {b}^{2} - ab) + b( {a}^{2} + {b}^{2} - ab)\\ \\ = > {a}^{ 3} + {b}^{3} = a \times {a}^{2} + a \times {b}^{2} + a \times - ab + b \times {a}^{2} + b \times {b}^{2} + b \times - ab \\ \\ = > {a}^{3} + {b }^{ 3} = {a}^{3} + a {b}^{2} - {a}^{2} b + {a}^{2} b + {b}^{3} - a {b}^{2} \\ \\ cancelling \: the \: similar\: terms \: with \: opposite \: signs \\ \\ = > {a}^{3} + {b}^{3} = {a}^{3} + {b}^{3}$

$\color{brown}\underline\textbf{Hence, proved. }$

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A cube plus b cube is equal to what

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