题目

七下数学因式分解
1.3(x-1)3y-(1-x)
2.（2a+b)(2a-3b)-3a(2a+b)
3.6xy-9x²y
4.（a+b)(a-b)-(b+a)
5.a(x-a)+b(a-x)c(x-a)
6.2x(x+y)²-(x+y)
7.m²(x-2)+m(2-x)
8.100-(3x+2y)²
9.x⁴-18x²+81
10.9x⁴-36y²
11.x²-4xy-1+4y²
12.9x⁴-36y²
13.(1-a)mn+a-1
14.m²(p-q)-p+q
15.x⁴y²-6x²y²+9y²
16.(x²+4)²-16x²
17.a³-12a²b+36ab²
18.x⁴-2x³-35x²
19.（x+y)⁴-(x-y)⁴
20.4b²c²-(b²+c²-a²)²
21.x²-6xy+9y²-3x+9y+2
22.9m²-25n⁴
23.8a-4a²-4
24.2ab-a²b²-1+c²

提问时间：2020-10-06

答案

1.3(x-1)3y-(1-x)=3(x-1)3y+ (x-1)=(9y+1)(x-1)
2.（2a+b)(2a-3b)-3a(2a+b)=(2a+b)(2a-3b-3a)=-(2a+b)(a+3b)
3.6xy-9x²y=3xy(2-3x)
4.（a+b)(a-b)-(b+a)=(a+b)(a-b-1)
5.a(x-a)+b(a-x)-c(x-a)=(x-a)(a-b-c)
6.2x(x+y)²-(x+y)=(x+y)(2x²+2xy-1)
7.m²(x-2)+m(2-x)=m(x-2)(m-1)
8.100-(3x+2y)²=(10+3x+2y)(10-3x-2y)
9.x⁴-18x²+81=(x²-9) ²=(x+3) ²(x-3) ²
10.9x⁴-36y²=9(x²+2y)(x²-2y)
11.x²-4xy-1+4y²=(x-2y) ²-1=(x-2y+1)(x-2y-1)
12.9x⁴-36y²=9(x²+2y)(x²-2y)
13.(1-a)mn+a-1=(a-1)(1-mn)
14.m²(p-q)-p+q=(p-q)(m²-1)=(p-q)(m+1)(m-1)
15.x⁴y²-6x²y²+9y²=y²(x⁴-6x²+9)=y²(x²-3) ²
16.(x²+4)²-16x²=(x²+4+4x²)(x²+4-4x²)=(5x²+4)(4-3x²)
17.a³-12a²b+36ab²=a(a²-12ab+36b²)=a(a-6b) ²
18.x⁴-2x³-35x²=x²(x²-2x-35)=x²(x+5)(x-7)
19.（x+y)⁴-(x-y)⁴=[(x+y) ²+(x-y) ²][(x+y) ²-(x-y) ²]=8xy(x²+y²)
20.4b²c²-(b²+c²-a²)²=(2bc+b²+c²-a²)(2bc-b²-c²+a²)
=-[(b+c) ²-a²][(b-c) ²-a²]
=-(b+c+a)(b+c-a)(b-c+a)(b-c-a)
21.x²-6xy+9y²-3x+9y+2
=(x-3y) ²-3(x-3y)+2
=(x-3y-1)(x-3y-2)
22.9m²-25n⁴=(3m+5n²)(3m-5n²)
23.8a-4a²-4=-4(a²-2a+1)=-4(a-1) ²
24.2ab-a²b²-1+c²=c²-(a²b²-2ab+1)=c²-(ab-1) ²=(c+ab-1)(c-ab+1)