Question

ए प्लस बी प्लस सी का होल क्यूब​

Answer 1

$\downarrow \\ \sf {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca$

Answer 2

Answer:

${(a + b + c)}^{3} = \: {(a + d)}^{3} \: \: where \: d = (b + c) \\ \\ \\ {(a + d)}^{3} = {a}^{3} + {d}^{3} + 3 {a}^{2} d + 3 a{d}^{2} \\ \\ \\ replacing \: d \: by \: ( b+ c) \\ \\ {(a + b + c)}^{3} = {a}^{3} + {(b + c)}^{3} + 3 {a}^{2} (b + c) + 3a {(b + c)}^{2} \\ \\ \\ = {a}^{3} + {b}^{3} + {c}^{3} + 3 {b}^{2} c + 3b {c}^{2} + 3 {a}^{2} b + 3 {a}^{2} c + 3a( {b}^{2} + {c}^{2} + 2bc) \\ \\ \\ = {a}^{3} + {b}^{3} + {c}^{3} + 3 {b}^{2} c + 3b {c}^{2} + 3 {a}^{2} b + 3 { a}^{2} c + 3a {b}^{2} + 3a {c}^{2} + 6abc \\ \\ \\ \\ \underline{ \large{thus}} \\ \\ \\ { \large{ \pink{ \boxed{ \sf{{(a + b + c)}^{3} = {a}^{3} + {b}^{3} + {c}^{3} + 3 {b}^{2} c + 3b {c}^{2} + 3 {a}^{2} b + 3 { a}^{2} c + 3a {b}^{2} + 3a {c}^{2} + 6abc}}}}}$