Scomporre i seguenti polinomi:

1) $\displaystyle a^6-b^3=(a^2-b)(a^4+a^{2}b+b^2)$

2) $\displaystyle -\frac{1}{8}a^3+8=$

$\displaystyle =\left(2-\frac{1}{2}a\right)\left(4+a+\frac{1}{4}a^2\right)$

3) $\displaystyle x^6-8y^3=(x^2-2y)(x^4+2x^{2}y+4y^2)$

4) $\displaystyle a^3+27=(a+3)(a^2-3a+9)$

5) $\displaystyle 125a^3+8=(5a+2)(25a^2-10a+4)$

6) $\displaystyle x^3-\frac{1}{8}=\left(x-\frac{1}{2}\right)\left(x^2+\frac{1}{2}x+\frac{1}{4}\right)$

7) $\displaystyle 8^{-1}p^3-2^6=$

$\displaystyle =\frac{1}{8}p^3-64=$

$\displaystyle =\left(\frac{1}{2}p-4\right)\left(\frac{1}{4}p^2+2p+16\right)$

8) $\displaystyle 0,001-u^6v^3=$

$\displaystyle =\frac{1}{1000}-u^6v^3=$

$\displaystyle =\left(\frac{1}{10}-u^2v\right)\left(\frac{1}{100}+\frac{1}{10}u^2v+u^4v^2\right)$

9) $\displaystyle x^{3n}-8=(x^{n}-2)(x^{2}+2x^{n}+4)$

10) $\displaystyle a^{3x}+a^6=(a^{x}+a^2)(a^{2x}-a^{x+2}+a^4)$

11) $\displaystyle a^{6n}-a^3=(a^{2n}-a)(a^{4n}+a^{2n+1}+a^2)$

12) $\displaystyle x^{6n}y^{3n}-1=(x^{2n}y^{n}-1)(x^{4n}y^{2n}+x^{2n}y^{n}+1)$