Question

Without actually calculating the cubes, find the value of (25)^3-(75)^3+(50)^3

Answer 1

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BY IDENTITY...

IF

$x + y + z = 0$

THEN

${x}^{3} + {y}^{3} + z {}^{3} = 3xyz$

BY APPLYING THIS...WE GET...

$25 - 75 + 50 = ( - 50) + 50 = 0$

THEREFORE ANSWER IS....

$3(25)( - 75)(50) = - 281250$

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