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Qual é il risultato ?

1 + 3 * 1^2 *(-2/3 a^3) + 3* 1 * (-2/3 a^3)^2 - 8/27 a^9 +

+ 4a^2 + 1/4 a^4 + 2a^3 - 1/4 a^4 + 8/27 a^9 - 4/3 a^6 = 

= 1 - 2a^3 - 4/3 a^6 + 4a^2 + 2a^3 - 4/3 a^6 = 1 + 4a^2

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$\small \left(1-\dfrac{2}{3}a^3\right)^3+\left(2a+\dfrac{1}{2}a^2\right)-\dfrac{1}{3}\left(-a\right)^4·\left(\dfrac{3}{4}-\dfrac{8}{9}a^5\right)-\dfrac{4}{3}a^6=$

$\small = 1-2a^3+\dfrac{4}{3}a^6-\dfrac{8}{27}a^9+4a^2+2a^3+\dfrac{1}{4}a^4-\dfrac{1}{3}a^4·\left(\dfrac{3}{4}-\dfrac{8}{9}a^5\right)-\dfrac{4}{3}a^6=$

$\small = 1\cancel{-2a^3}\cancel{+\dfrac{4}{3}a^6}-\dfrac{8}{27}a^9+4a^2\cancel{+2a^3}+\dfrac{1}{4}a^4-\dfrac{1}{3}a^4·\left(\dfrac{3}{4}-\dfrac{8}{9}a^5\right)\cancel{-\dfrac{4}{3}a^6}=$

$\small = 1-\dfrac{8}{27}a^9+4a^2+\dfrac{1}{4}a^4-\dfrac{1}{3}a^4·\left(\dfrac{3}{4}-\dfrac{8}{9}a^5\right)=$

$\small = 1-\dfrac{8}{27}a^9+4a^2+\dfrac{1}{4}a^4-\dfrac{1}{4}a^4+\dfrac{8}{27}a^9=$

$\small = 1\cancel{-\dfrac{8}{27}a^9}+4a^2\cancel{+\dfrac{1}{4}a^4}\cancel{-\dfrac{1}{4}a^4}\cancel{+\dfrac{8}{27}a^9} =$

$\small = 1+4a^2 $

(1 - 2/3·a^3)^3 + (2·a + 1/2·a^2)^2 - 1/3·(-a)^4·(3/4 - 8/9·a^5) - 4/3·a^6=

=(- 8·a^9/27 + 4·a^6/3 - 2·a^3 + 1) + (a^4/4 + 2·a^3 + 4·a^2) - 1/3·a^4·(3/4 - 8/9·a^5) - 4/3·a^6=

=(- 8·a^9/27 + 4·a^6/3 - 2·a^3 + 1) + (a^4/4 + 2·a^3 + 4·a^2) - (a^4/4 - 8·a^9/27) - 4/3·a^6=

=4·a^2 + 1