Scomporre i seguenti polinomi:

1) $\displaystyle -a^4+b^2=(b+a^2)(b-a^2)$

2) $\displaystyle \frac{1}{4}x^6-\frac{1}{9}y^2=\left(\frac{1}{2}x^3+\frac{1}{3}y\right)\left(\frac{1}{2}x^3-\frac{1}{3}y\right)$

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

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

5) $\displaystyle -81a^4+4^{-2}=-81a^4+\left(\frac{1}{4}\right)^2=$

$\displaystyle=\left(\frac{1}{4}+9a^2\right)\left(\frac{1}{4}-9a^2\right)=$

$\displaystyle =\left(\frac{1}{4}+9a^2\right)\left(\frac{1}{2}+3a\right)\left(\frac{1}{2}-3a\right)$

6) $\displaystyle (x+1)^2-y^2=(x+1+y)(x+1-y)$

7) $\displaystyle 4m^4-(m+n)^2=(2m^2+m+n)(2m^2-m-n)$

8) $\displaystyle a^2-4a+4-9b^2=$

$\displaystyle =(a-2)^2-9b^2=$

$\displaystyle =(a-2+3b)(a-2-3b)$

9) $\displaystyle \frac{1}{4}-m^2+6mn-9n^2=$

$\displaystyle =-\left(-\frac{1}{4}+m^2-6mn+9n^2\right)=$

$\displaystyle =-\left[\left(m-3n\right)^2-\frac{1}{4}\right]=$

$\displaystyle =-\left[\left(m-3n+\frac{1}{2}\right)\left(m-3n-\frac{1}{2}\right)\right]$