a)x^4+2x³-2x²-1
=(x²)²-1+2x³-2x²
=(x²-1)(x²+1)+2x³-2x²
=(x-1)(x+1)(x²+1)+2x²(x-1)
=(x-1)[(x+1)(x²+1)+2x²]
=(x-1)[x³+x+x²+1+2x²]
=(x-1)[x³+3x²+x+1]
=(x-1)(x³+3x²+x+1)
b)x²+2x-4y²-4y
=x²+2x+1-(2y)²-2.y.2-1
=(x²+2x+1)-[(2y)²+2.y.2+1]
=(x+1)²-(2y+1)²
=[(x+1)-(2y+1)][(x+1)+(2y+1)]
=(x+1-2y-1)(x+1+2y+1)
=(x-2y)(x+2y+2)
c)a²(b-c)+b²(c-a)+c²(a-b)
=a²b-a²c+b²c-ab²+ac²-bc²
=a²b-ab²-a²c+b²c+ac²-bc²
=ab(a-b)-c(a²-b²)+c²(a-b)
=ab(a-b)-c(a-b)(a+b)+c²(a-b)
=(a-b)[ab-c(a+b)+c²]
=(a-b)(ab-ac-bc+c²)
=(a-b)(ab-bc-ac+c²)
=(a-b)[b(a-c)-c(a-c)]
=(a-b)[(a-c)(b-c)]
=(a-b)(a-c)(b-c)
d)(x-y)³+(x-z)³+(z-x)³
=x³-3x²y+3xy²-y³+{(x-z+z-x)[(x-z)²-(x-z)(z-x)+(z-x)²}
=x³-3x²y+3xy²-y³+(0.[(x-z)²-(x-z)(z-x)+(z-x)²]
=x³-3x²y+3xy²-y³+0
=x³-3x²y+3xy²-y³
Chúc bạn học tốt!!! ^_^ ^_^ ^_^
