:Scomporre i seguenti polinomi

1) $\displaystyle 4y^2+4xy+12yz+x^2+6xz+9z^2=$

$\displaystyle =(2y+x+3z)^2$.

2) $\displaystyle \frac{1}{4}a^2-2ab-ac+4b^2+4bc+c^2=$

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

3) $\displaystyle \frac{1}{4}a^6-a^5+a^4+2a^3-4a^2+4=$

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

4) $\displaystyle -9x^2-4y^2-1-12xy-6x-4y=$

$\displaystyle =-(9x^2+4y^2+1+12xy+6x+4y)=$

$\displaystyle =-(3x+2y+1)^2$.

5) $\displaystyle -9x^2-4y^2-1-12xy+6x+4y=$

$\displaystyle =-(9x^2+4y^2+1+12xy-6x-4y)=$

$\displaystyle =-(3x+2y-1)^2$.