Question

prove that acube+bcube=(a+b) (a square+b square-ab)​

Answer 1

$\huge \sf {\orange {\underline {\pink{\underline {A᭄ɴsᴡᴇʀ࿐ :−}}}}}$

$\boxed{ \red{\begin{gathered} \bf To \: prove \: {a}^{3} + {b}^{3} = (a + b)( {a}^{2} + {b}^{2} - ab) \\ \\ {a}^{3} + {b}^{ 3} a( {a}^{2} + {b}^{2} - ab) + b( {a}^{2} + {b}^{2} - ab)\\ \\ {a}^{ 3} + {b}^{3} = a \times {a}^{2} + a \times {b}^{2} + a \times - ab + b \times {a}^{2} + b \times {b}^{2} + b \times - ab \\ \\{a}^{3} + {b }^{ 3} = {a}^{3} + a {b}^{2} - {a}^{2} b + {a}^{2} b + {b}^{3} - a {b}^{2} \\ \bf Cancelling \: the \: similar\: terms \: with \: opposite \: signs \\ \\ {a}^{3} + {b}^{3} = {a}^{3} + {b}^{3} \end{gathered}} }\\ \color{brown}\underline\textbf{Hence, proved. }$

Answer 2

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×a

2

+a×b

2

+a×−ab+b×a

2

+b×b

2

+b×−ab

a

3

+b

3

=a

3

+ab

2

−a

2

b+a

2

b+b

3

−ab

2

Cancelling the similar terms with opposite signs

a

3

+b

3

=a

3

+b

3

Hence, proved.