Question

Descompuneti in factori:
1. x²(x+1) + x(x+1)² =?
2. xy-x-y+1 =?
3. 9xy+3x-3y-1 =?
4. x²+6x+9-y² =?
5. 2x²+x-1 =?
6. x³+x²-16x-16 =?                                                                                                                                                                  

Answer 1

1. x²(x+1) + x(x+1)² = x(x+1)(x+1)=x(x+1)²

2. xy-x-y+1 =x(y-1) - (y-1)=(y-1)(x-1)

3. 9xy+3x-3y-1 =3x(3y+1)-(3y+1)=(3y+1)(3x-1)

4. x²+6x+9-y² =(x+3)²-y²=(x+3+y)(x+3-y)=(x+y+3)(x-y+3)

5. 2x²+x-1 = x²-1+x²+x=(x+1)(x-1)+x(x+1)=(x+1)(x-1+x)=(x+1)(2x-1)

6. x³+x²-16x-16 =x(x²-16)+(x²-16) = (x²-16)(x+1)=(x+1) (x-1)(x+1)=(x+1)²(x-1)