Prove that (a+b+c)whole cube - a cube -b cube - c cube = 3(a+b)(b+c)(c+a )

CBSE Class 9 CBSE Class 9 Maths
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prove that (a+b+c)whole cube - a cube -b cube - c cube = 3(a+b)(b+c)(c+a)

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open parentheses a plus b plus c close parentheses cubed minus a cubed minus b cubed minus c cubed equals open square brackets open parentheses a plus b plus c close parentheses cubed minus a cubed close square brackets minus open square brackets b cubed plus c cubed close square brackets equals open square brackets open parentheses b plus c close parentheses open parentheses open parentheses a plus b plus c close parentheses squared plus open parentheses a plus b plus c close parentheses a plus a squared close parentheses close square brackets minus open square brackets open parentheses b plus c close parentheses open parentheses b squared minus b c plus c squared close parentheses close square brackets equals open parentheses b plus c close parentheses open square brackets open parentheses open parentheses a plus b plus c close parentheses squared plus open parentheses a plus b plus c close parentheses a plus a squared close parentheses minus open parentheses b squared minus b c plus c squared close parentheses close square brackets equals open parentheses b plus c close parentheses open square brackets 3 a squared plus 3 a b plus 3 b c plus 3 c a close square brackets equals 3 open parentheses b plus c close parentheses open square brackets a squared plus a b plus b c plus c a close square brackets equals 3 open parentheses b plus c close parentheses open square brackets a open parentheses a plus b close parentheses plus c open parentheses b plus a close parentheses close square brackets equals 3 open parentheses b plus c close parentheses open parentheses a plus b close parentheses open parentheses a plus c close parentheses