Question

$Descompuneti~in ~factori:\\ y^2-3y+2;\\ a^2y^2-5a^2y+6a^2;\\ x^2y-yx-2x+2;\\ a^2+a^2b-3a-3ab;$

Answer 1

$a) =y^2-y-2y+2=(y^2-y)-(2y-2)=y(y-1)-2(y-1)=$
$=(y-2)(y-1)$

$b) =a^2y^2-2a^2y-3a^2y+6a^2=(a^2y^2-2a^2y)-(3a^2y-6a^2)=$
$=y(a^2y-2a^2)-3(a^2y-2a^2)=(y-3)(a^2y-2a^2)$

$c) =(x^2y-yx)-(2x-2)=xy(x-1)-2(x-1)=(yx-2)(x-1)$

$d) =(a^2+a^2b)-(3a+3ab)=a^2(1+b)-3a(1+b)=(a^2-3a)(1+b)$

Answer 2

     
$Descompuneti~in ~factori:\\ y^2-3y+2 =y^2-y-2y+2 = y(y-1)-2(y-1)=(y-1)(y-2) \\ \\ a^2y^2-5a^2y+6a^2= a^{2}(y^2-2y-3y+6)= \\ =a^{2}(y(y-2)-3(y-2)=a^{2}(y-2)(y-3) \\ \\ x^2y-yx-2x+2 = xy(x-1)-2(x-1)=(x-1)(xy-2) \\ \\ a^2+a^2b-3a-3ab=a^2(1+b)-3a(1+b)= \\ =(1+b)(a^2-3a)=a(a-3)(1+b)$