Question

数学的因式分解题，急求解！！请帮忙！！

分解因式：①x^4-12x+323
②x^4+7x³+14x²+7x+1
③(x²-3x-3)(x²+3x+4)-8
④x²y²+1-x²-y²+4xy
⑤x^4+x²-2ax-a²+1
⑥（x+y）^4+x^4+y^4
⑦a³b-ab³+a²+b²+1
速度速度！！！

Answer 1

①
x^4-12x+323
=x^4+324-12x-1
=(x^4+36x^2+324)-(36x^2+12x+1)
=(x^2+18)^2-(6x+1)^2
=(x^2+18+6x+1)(x^2+18-6x-1)
=(x^2+6x+19)(x^2-6x+17)
②
x^4+7x^3+14x^2+7x+1
= x^4+7x^3+12x^2 + 2x^2+7x + 1
= (x^2+3x)(x^2+4x) + x^2+3x + x^2+4x + 1
=(x^2+3x)(x^2+4x+1)+(x^2+4x+1)
= (x^2+3x+1)*(x^2+4x+1)
③
(x^2-3x-3)(x^2+3x+4)-8在有理数系数的范围内无法分解，根据因式定理
④
x^2y^2+1-x^2-y^2+4xy
=x^2y^2+2xy+1-x^2-y^2+2xy
=(xy+1)^2-(x-y)^2
=(xy+1+x-y)(xy+1-x+y)
⑤
x^4+x^2+2ax+1-a^2
= x^4+2x^2+1-x^2+2ax-a^2
=(x^2+1)^2-(x-a)^2
=(x^2+1+x-a)(x^2+1-x+a)
⑥
(x+y)^4+x^4+y^4
=(x^2+2xy+ y^2)^2+x^4+y^4
= x^4+y^4+4x^2y^2+2x^2y^2+4x^3y+4xy^3+ x^4+y^4
=2[x^4+y^4+3x^2y^2+2xy(x^2+ y^2))]
=2[x^4+y^4+2x^2y^2+2xy(x^2+ y^2)+ x^2y^2]
=2[(x^2+y^2)^2+2xy(x^2+ y^2)+ (xy)^2]
=2(x^2+ y^2+xy)^2
⑦
a^3b-ab^3+a^2+b^2+1
=a^3b-a^2b^2+a^2b^2+ab-ab-ab^3+a^2+b^2+1
=a^3b-a^2b^2+ab+a^2b^2-ab^3+b^2+a^2-ab+1
=ab(a^2-ab+1)+b^2(a^2-ab+1)+1(a^2-ab+1)
=(ab+b^2+1)(a^2-ab-1)

追问

那下面这个怎么做？
2x²-xy-3y²-6x+14y-8

追答

2x^2-xy-3y^2-6x+14y-8
=2x^2-xy-3y^2 -8x+12y +2x+2y -8
=(x+y)(2x-3y) -4(2x-3y) +2(x+y) -8
=(x+y-4)(2x-3y+2)