Solve ${(x^{3} + 1)}^{3} + 2 x^{2} - 6 x (x^{3} + 2)$

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Solution

Given that:
$(x^{3} + 1)^{3} + 2 x^{2} - 6 x (x^{3} + 2)$
On expanding, we get
$= x^{9} + 1 + 3 x^{6} + 3 x^{3} + 2 x^{2} - 6 x^{4} - 12 x$

$= x^{9} + 1 + 3 x^{6} + 3 x^{3} + 2 x^{2} - 6 x^{4} - 12 x$

$= x^{9} + 3 x^{6} - 6 x^{4} + 3 x^{3} + 2 x^{2} - 12 x + 1$

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Solve (x3+1)3+2x2−6x(x3+2)

Given that:(x3+1)3+2x2−6x(x3+2)On expanding, we get=x9+1+3x6+3x3+2x2−6x4−12x=x9+1+3x6+3x3+2x2−6x4−12x=x9+3x6−6x4+3x3+2x2−12x+1

Solve ${(x^{3} + 1)}^{3} + 2 x^{2} - 6 x (x^{3} + 2)$

Given that:
$(x^{3} + 1)^{3} + 2 x^{2} - 6 x (x^{3} + 2)$
On expanding, we get
$= x^{9} + 1 + 3 x^{6} + 3 x^{3} + 2 x^{2} - 6 x^{4} - 12 x$

$= x^{9} + 1 + 3 x^{6} + 3 x^{3} + 2 x^{2} - 6 x^{4} - 12 x$

$= x^{9} + 3 x^{6} - 6 x^{4} + 3 x^{3} + 2 x^{2} - 12 x + 1$