Question

Descompuneti in factori:
x²-2x+1-y²=
x²-4y²+6x+9=
16x²-16y²-8x+1=
4x²-9y²+6y-1=
x²-y²-4yz-4z²=
x⁴-25+2x³+x²=
(x²+y²-z²)²-4x²y²=
25a²-4b²+12bc-9c²=

Answer 1

(x-1)²-y²=(x-1-y)(x-1+y)
(x+3)²-4y²=(x+3-2y)(x+3+2y)
(4x-1)²-16y²=(4x-1-4y)(4x-1+4y)
x²-(y-2z)²=(x-y+2z)(x+y-2z)
x²(x+1)²-25=(x²+x-5)(x²+x+5)
(x²+y²-z²-2x²y²)(x²+y²-z²+2x²y²)
25a²-(4b²-12bc+9c²)=25a²-(2b-3c)²=(5a-2b+3c)(5a+2b-3c)
4x²-(9y²-6y+1)=4x²-(3y-1)²=(2x-3y+1)(2x+3y-1)

1)=x²-6x-7x+42=x(x-6)-7(x-6)=(x-6)(x-7)
2)=x²+2x-11x-22=x(x+2)-11(x+2)=(x+2)(x-11)
3)=x²+5x-20x-100=x(x+5)-20(x+5)=(x+5)(x-20)
4)=x²+2x-25x-50=x(x+2)-25(x+2)=(x+2)(x-25)
5)=x²-2x+13-26=x(x-2)+13(x-2)=(x-2)(x+13)
6)=x²+4x-20x-80=x(x+4)-20(x+4)=(x+4)9x-20)
7)=x²-x+20x-20=x(x-1)+20(x-1)=(x-1)(x+20)