Răspuns:
1. a) (x-1)(x²+1)
b) (x+1)²×(x-1)
c) (x+2)(x²+3)
2. a) (y-3)(x-4)
b) (y-3)(2x+1)
c) (3y+2)(2x-1)
3. a) (x²+2)(a²+2)
b) (x-2)(y+2)(x-3)(x+3)
c) (y-2)(y+2)(x²+1)
Explicație pas cu pas:
1. a) x²(x-1)+x-1 =
= (x-1)(x²+1)
b) x²(x+1)-(x+1) =
= (x+1)(x²-1) =
= (x+1)(x-1)(x+1) =
= (x+1)²×(x-1)
c) x²(x+2)+3(x+2) =
= (x+2)(x²+3)
2. a) x(y-3)-4(y-3) =
= (y-3)(x-4)
b) 2x(y-3)+y-3 =
= (y-3)(2x+1)
c) 2x(3y+2)-(3y+2) =
= (3y+2)(2x-1)
3. a) a²(x²+2)+2(x²+2) =
= (x²+2)(a²+2)
b) x²(y²-4)-9(y²-4) =
= (y²-4)(x²-9) =
= (y-2)(y+2)(x-3)(x+3)
c) x²(y²-4)+y²-4 =
= (y²-4)(x²+1) =
= (y-2)(y+2)(x²+1)
