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# Without actually calculating the cubes, find the value of the following: (i) ( - 12)^3 + (7)^3 + (5)^3

14.(i)  Without actually calculating the cubes, find the value of each of the following:
(i)  $(-12)^3 + (7)^3 + (5)^3$

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Given is   $(-12)^3 + (7)^3 + (5)^3$

We know that

If   $x+y+z = 0$   then ,   $x^3+y^3+z^3 = 3xyz$

Here, $x = -12 , y = 7 \ \ an d \ \ z = 5$

$\Rightarrow x+y+z = -12+7+5 = 0$

Therefore,

$(-12)^3 + (7)^3 + (5)^3 = 3 \times (-12)\times 7 \times 5 = -1260$

Therefore, value of  $(-12)^3 + (7)^3 + (5)^3$  is  $-1260$

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