Question

evaluate using identity 55 cube minus 25 cube minus 30 cube

Answer 1

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$We \:know \: that , \\</p><p>\pink { If \: x + y + z = 0 } \:then \\ \green { x^{3}+y^{3} +z^{3} = 3xyz }$

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$Here , x = 55, y = -25 \ : and \: z = -30$

$x + y + z \\= 55 + (-25 )+ (-30 ) \\= 55 - 25 - 30 \\= 0$

$Now , Value \:of \: 55^{3} - 25^{3} - 30^{3}\\= 55^{3} + (-25)^{3} +(- 30)^{3} \\= 3 \times 55\times (-25) \times (-30) \\= 123750$

Therefore.,

$\red {Value \:of \: 55^{3} - 25^{3} - 30^{3}}\\\green {= 1,23,750 }$

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