Question

几道有关因式分解的题目

如题。谢谢！

Answer 1

1.
(1)
=[2(x²+6x+1)+(x²+1)][(x²+6x+1)+2(x²+1)]
=(2x²+12x+2+x²+1)(x²+6x+1+2x²+2)
=(3x²+12x+3)(3x²+6x+3)
=9(x²+4x+1)(x+1)²

(2)
=(x²+8x+7)(x²+8x+15)+15
=(x²+8x)²+22(x²+8x)+105+15
=(x²+8x)²+22(x²+8x)+120
=(x²+8x+12)(x²+8x+10)
=(x+2)(x+6)(x²+8x+10)

2.
x³+y³+3xy
=(x+y)(x²-xy+y²)+3xy
=1*(x²+2xy+y²-3xy)+3xy
=(x+y)²-3xy+3xy
=1²
=1

3.
ω^1980+ω^1981+ω^1982+....+ω^2000
=ω^1980(1+ω+ω²)+ω^1983(1+ω+ω²)+.....+ω^1998(1+ω+ω²)
=ω^1980*0+ω^1983*0+....+ω^1998*0
=0

4.
∵a³+a²c+b²c-abc+b³
=(a³+b³)+(a²c+b²c-abc)
=(a+b)(a²-ab+b²)+c(a²-ab+b²)
=(a²-ab+b²)(a+b+c)
∵a+b+c=0
∴
a³+a²c+b²c-abc+b³=(a²-ab+b²)(a+b+c)=0