因式分解分压在这儿越快越好32ac²+15cx²-48ax²-10c³（ax+by）²+（ay-bx）²+c²x²+c²y²1+（b-a²）x²-abx²ab（c²-d²）-（a²-d²）cdx²y²z²

Question

因式分解 分压在这儿 越快越好
32ac²+15cx²-48ax²-10c³
（ax+by）²+（ay-bx）²+c²x²+c²y²
1+（b-a²）x²-abx²
ab（c²-d²）-（a²-d²）cd
x²y²z²-x²z-y²z+1
6ax²-9a²xy+2xy-3ay²
5x³-15x²-x+3
5a²m-15am+3bm-9bm
x3-2x²-x+2+x5-2x4
x²-x-9y²-3y
x5+y5-(x4y+xy4)
-1-2x-x²+y²
x12-3x6+1
x8+x4+1
答得越多越好

Answer 1

①原式=(32ac²-48ax²)-(10c³-15cx²)=16a(2c²-3x²)-5c(2c²-3x²)
=(16a-5c)(2c²-3x²)[有理数范围]=(16a-5c)(√2c+√3x)(√2c-√3x)
②原式=a²x²+b²y²+a²y²+b²x²+c²x²+c²y²=(a²x²+b²x²+c²x²)+(a²y²+b²y²+c²y²)
=x²(a²+b²+c²)+y²(a²+b²+c²)=(a²+b²+c²)(x²+y²)
1+(b-a²)x²-abx²；ab(c²-d²)-(a²-d²)cd题目有误
⑤原式=(x²y²z²-x²z)-(y²z-1)=x²z(y²z-1)-(y²z-1)=(x²z-1)(y²z-1)
⑥原式=(6ax²-9a²xy)+(2xy-3ay²)=3ax(2x-3ay)+y(2x-3ay)=(3ax+y)(2x-3ay)
⑦原式=(5x³-15x²)-(x-3)=5x²(x-3)-(x-3)=(x-3)(5x²-1)=(x-3)(√5x+1)(√5x-1)
⑧原式=5a²m-15am-6bm=m(5a²-15a-6b)
⑨原式=(x³-2x²)-(x-2)+(x^5-2x⁴)=x²(x-2)-(x-2)+x⁴(x-2)=(x-2)(x⁴+x²+1)
=[(x²+1)²-x²](x-2)=(x-2)(x²+x+1)(x²-x+1)
⑩原式=(x²-9y²)-(x+3y)=(x+3y)(x-3y)-(x+3y)=(x+3y)(x-3y-1)
x^5+y^5-(x⁴y+xy⁴)=(x^5-x⁴y)-(xy⁴-y^5)=x⁴(x-y)-y⁴(x-y)=(x-y)(x⁴-y⁴)
=(x-y)(x²+y²)(x²-y²)=(x+y)(x²+y²)(x-y)²
-1-2x-x²+y²=y²-(x²+2x+1)=y²-(x+1)²=(y+x+1)(y-x-1)
x¹²-3x^6+1=(x^6-1)²-x^6=(x^6+x³-1)(x^6-x³-1)[有理数范围内]
x^8+x⁴+1=(x⁴+1)²-x⁴=(x⁴+x²+1)(x⁴-x²+1)=(x²+x+1)(x²-x+1)(x²+√3x+1)(x²-√3x+1)