Question

use suitable identity, find the value of (42)^3-(24)^3-(18)^3​

Answer 1

$We \:know \:that, \\If \:x+y+z = 0 ,\:then \\x^{3} + y^{3} + z^{3} = 3xyz$

$Here , x = 42 , y = -24 , z = -18$

$x + y + z \\= 42 + (-24) + (-18) \\= 42 - 24 - 18 \\= 0$

$Now, Value \: of \: 42^{3} - (24)^{3} - (18^{3}) \\= 42^{3} + (-24)^{3} + (-18)^{3} \\= 3 \times 42 \times (-24 ) \times (-18) \\= 54432$

Therefore.,

$\red { Value \:of \:42^{3} - (24)^{3} - (18^{3})} \green { = 54432 }$

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