Scomporre i seguenti polinomi mediante raccoglimento totale e raccoglimento parziale-totale:

1) $\displaystyle 50x^2-10x-5x^3=$

$\displaystyle =5x(10x-2-x^2)$

2) $\displaystyle 4x^2y^2+6xy=$

$\displaystyle =2xy(2xy+3)$

3) $\displaystyle x(y-6)-7(y-6)=(y-6)(x-7)$

4) $\displaystyle 2ab+2a+b^2+b=$

$\displaystyle =2a(b+1)+b(b+1)=$

$\displaystyle =(b+1)(2a+b)$

5) $\displaystyle abx^2+2abx-abxy-2aby=$

$\displaystyle =ab(x^2+2x-xy-2y)=$

$\displaystyle =ab[x(x+2)-y(x+2)]=$

$\displaystyle = ab(x+2)(x-y)$

6) $\displaystyle 3a^2y^2-3axy^2-3xy^2+3a^3y^2=$

$\displaystyle =3y^2(a^2-ax-x+a^3)=$

$\displaystyle =3y^2[a^2(1+a)-x(a+1)]=$

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

7) $\displaystyle 6ax^2-6ax+6a+6x^2-6x+6=$

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

$\displaystyle =6[a(x^2-x+1)+1(x^2-x+1)]=$

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

8) $\displaystyle 4a^2+a-8ab-8b+4c(a+1)=$

$\displaystyle =4[a^2+a-2ab-2b+c(a+1)]=$

$\displaystyle =4[a(a+1)-2b(a+1)+c(a+1)]=$

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

9) $\displaystyle -3x^5y-6x^3y^3-x^4y^2-2x^2y^4+7x^4y+14x^2y^3=$

$\displaystyle =x^2y(-3x^3-6xy^2-x^2y-2y^3+7x^2+14y^2)=$

$\displaystyle =x^2y[x^2(-3x-y+7)+2y^2(-3x-y+7)]=$

$\displaystyle =x^2y(-3x-y+7)(x^2+2y^2)$