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प्रश्न
Verify the following:
(a + b + c)(a2 + b2 + c2 – ab – bc – ca) = a3 + b3 + c3 – 3abc
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उत्तर
Taking L.H.S. = (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
= a(a2 + b2 + c2 – ab – bc – ca) + b(a2 + b2 + c2 – ab – bc – ca) + c(a2 + b2 + c2 – ab – bc – ca) ...[Distributive law]
= a3 + ab2 + ac2 – a2b – abc – a2c + ba2 + b3 + bc2 – b2a – b2c – bca + ca2 + cb2 + c3 – cab – c2b – c2a
= a3 + b3 + c3 – 3abc
= R.H.S.
Hence verified.
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