分解因式：（1）-3xy-9y^2-1/4x^2 (2)14a^2b-49a^3b-ab (3)a^4-2a^2b^2+b^4 (4)(x+y)^2+4(x-y)^2-4(x^2y^会几个打几个,(4)(x+y)^2+4(x-y)^2-4(x^2y^2)
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/20 11:15:24
分解因式：（1）-3xy-9y^2-1/4x^2 (2)14a^2b-49a^3b-ab (3)a^4-2a^2b^2+b^4 (4)(x+y)^2+4(x-y)^2-4(x^2y^会几个打几个,(4)(x+y)^2+4(x-y)^2-4(x^2y^2)
分解因式：（1）-3xy-9y^2-1/4x^2 (2)14a^2b-49a^3b-ab (3)a^4-2a^2b^2+b^4 (4)(x+y)^2+4(x-y)^2-4(x^2y^
会几个打几个,
(4)(x+y)^2+4(x-y)^2-4(x^2y^2)
分解因式：（1）-3xy-9y^2-1/4x^2 (2)14a^2b-49a^3b-ab (3)a^4-2a^2b^2+b^4 (4)(x+y)^2+4(x-y)^2-4(x^2y^会几个打几个,(4)(x+y)^2+4(x-y)^2-4(x^2y^2)
（1）-3xy-9y^2-1/4x^2
=-4(12xy+36y^2+x^2)
=-4(x+6y)^2
(2)14a^2b-49a^3b-ab
=-ab(-14a+49a^2+1)
=-ab(7a-1)^2
(3)a^4-2a^2b^2+b^4
=(a^2-b^2)^2
=[(a+b)(a-b)]^2
=(a+b)^2(a-b)^2
(4)(x+y)^2+4(x-y)^2-4(x^2-y^2)
=(x+y)^2-4(x^2-y^2)+4(x-y)^2
=(x+y)^2-4(x-y)(x+y)+4(x-y)^2
=[(x+y)-2(x-y)]^2
=(x+y-2x+2y)^2
=(3y-x)^2
（1）-3xy-9y^2-1/4x^2
=-（1/4x²+3xy+9y²）
=-（x/2+3y)²
2)14a^2b-49a^3b-ab
=-ab(49a²-14ab+1）
=-ab(7a-1）²
3)a^4-2a^2b^2+b^4
=（a²-b²）²
=（a+b)²(a-b)²
(4)(x+y)^2+4(x-y)^2-4(x^2y^
=
（1）-3xy-9y^2-1/4x^2=-(3y+1/2x)^2
(2)14a^2b-49a^3b-ab=-ab(49a^2-14a+1)=-ab(7a-1)^2
3)a^4-2a^2b^2+b^4=(a+b)^2(a-b)^2
(4)(x+y)^2+4(x-y)^2-4(x^2y^2)=
1.-3xy-9y^2-1/4x^2
=-(1/4x^2+3xy+9y^2)
=-(x/2+3y)^2
2.14a^2b-49a^3b-ab
=ab(14a-49a^2-1)
=-ab(49a^2-14a+1)
=-ab(7a-1)^2
3.a^4-2a^2b^2+b^4
=(a^2-b^2)^2
=(a+b)^2(a-b)^2
4.(x+y)^2+4(x-y)^2-4(x^2-y^2)
=(x+y-2(x-y))^2
=(-x+3y)^2