Question

求数学题因式分解追分紧急求在线等，望一小时内回复追分追分

1）x²+y²-x²y²-4xy-1
2）（x²+x+1）（x²+x+2)-12
3)x²+3ax+2a²-a-1
4)2x^3-x²Y-2y^3+xy²

Answer 1

1) 原式=(x^2-2xy+y^2)-(x^2y^2+2xy+1)=(x-y)^2-(xy+1)^2=(x-y+xy+1)(x-y-xy-1)
2) 原式=(x^2+x+1)^2+(x^2+x+1)-12=(x^2+x+1+4)(x^2+x+1-3)=(x^2+x+5)(x+2)(x-1)
3) 原式=(x^2+3ax+9/4*a^2)-(1/4*a^2+a+1)=(x+3a/2)^2-(a/2+1)^2=(x+3a/2+a/2+1)(x+3a/2-a/2-1)=(x+2a+1)(x+a-1)
4) 原式=2(x-y)(x^2+xy+y^2)-xy(x-y)=(x-y)(2x^2+xy+2y^2)

追问

第二个我不太懂可以详解吗？
第三格的*a^2是什么意思？

Answer 2

解：
1）
x^2+y^2-x^2y^2-4xy-1
=(x^2+y^2-2xy)-(x^2y^2+2xy+1)
=(x-y)^2-(xy+1)^2
=(x-y+xy+1)(x-y-xy-1)

2）
(x^2+x+1)(x^2+x+2)-12
=(x^2+x)^2+3(x^2+x)+2-12
=(x^2+x)^2+3(x^2+x)-10
=(x^2+x+5)(x^2+x-2)
=(x^2+x+5)(x+2)(x-1)

3）x²+3ax+2a^2-a-1
=x²+[(2a+1)+(a-1)]x+2a²-a-1
=x²+(2a+1)x+(a-1)x+(2a+1)(a-1)
=x[x+(2a+1)]+(a-1)[x+(2a+1)]
=[x+(2a+1)][x+(a-1)]

4）2x^3-x^2y-2y^3+xy^2
= 2x^3-2y^3+xy^2-x^2y
=2(x-y)(x^2+xy+y^2)+xy(y-x)
=(x-y)(2x^2+xy+2y^2)

追问

第二个不太懂，可以详解吗/

Answer 3

1）x² + y² - x²y² - 4xy - 1
= (x² + y² - 2xy) - (x²y² + 2xy + 1)
= (x - y)² - (xy + 1)²
= (x - y + xy + 1)(x - y - xy - 1)

2）设x2+x=y2，则
原式=(y+1)(y+2)-12=y2+3y-10
=(y-2)(y+5)=(x2+x-2)(x2+x+5)
=(x-1)(x+2)(x2+x+5)

3) x²+3ax+2a^2-a-1=0
=(x^2+3ax+9/4*a^2)-(1/4*a^2+a+1)
=(x+3a/2)^2-(a/2+1)^2
=(x+3a/2+a/2+1)(x+3a/2-a/2-1)
=(x+2a+1)(x+a-1)

4)2x^3-x²Y-2y^3+xy²
=2x^3-2y^3-xy(x-y)
=2(x-y)(x^2+xy+y^3)-xy(x-y)
=(x-y)(2x^2+2xy+2y^2-xy)
=(x-y)(2x^2+xy+2y^2)

追问

第三格的*a^2是什么意思？

Answer 4

1 (x-y-xy-1)(x-y+xy+1)
2 (x²+x+5)(x²+x-2)
3 4(2x-a+1)(2x+a+5)
4 (x-y)(2x²+2y²+xy)

Answer 5

第一个可不可以把X Y看成Sin 和Cos