Question

初一数学分组分解法~急！！！

1。分组时能应预见下一步分解的可能性1。______2._______3.________
2.分解因式(用分组分解):
x＾2-xy-2y＾2-x-y

x＾3+2x＾2-5x-6

a＾2-6ab+9b＾2-4a+12b+4

x＾2+2xy+y＾2-x-y-1/4

a＾2-10ab+25b＾2-5a+25b-6

3.对多项式4x＾2+2x-y＾2-y用分组分解法分解因式,下面分组分解正确的是( )
A.(4x＾2+2x)-(y＾2=y) B.4x＾2+(2x-y＾2-y)
C.(4x＾2-y＾2)+(2x-y) D.(4x＾2-y)(2x-y＾2)

4.将x＾3-x＾2+x-1分解因式时,错误的分组方法是( )
A.(x＾3-x＾2)+(x-1) B.(x＾3+x)+(-x＾2-1)
C.(x＾3-1)+(-x＾2+x) d.x＾3-(x＾2-x+1)

Answer 1

1. (分组后可直接提公因式)
(分组后可运用公式)
(分组后既可提公因式又可运用公式)
2. x＾2-xy-2y＾2-x-y
=(x＾2-y＾2)-(xy+y＾2)-(x+y)
=(x+y)(x-y)-y(x+y)-(x+y)
=(x+y)(x-y-y-1)
=(x+y)(x-2y-1)

x＾3+2x＾2-5x-6
=(x＾3+2x＾2+x)-(6x+6)
=x(x+1)＾2-6(x+1)
=(x+1)(x＾2+x-6)
=(x+1)[(x＾2+3x)-(2x+6)]
=(x+1)[x(x+3)-2(x+3)]
=(x+1)(x+3)(x-2)

a＾2-6ab+9b＾2-4a+12b+4
=(a＾2-6ab+9b＾2)-(4a-12b)+4
=(a-3b)＾2-4(a-3b)+4
=(a-3b-2)＾2

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

a＾2-10ab+25b＾2-5a+25b-6
=(a＾2-10ab+25b＾2)-(5a-25b)-6
=(a-5b)＾2-[(6a-30b)-(a-5b)]-6
=[(a-5b)＾2+(a-5b)]-6[(a-5b)+1]
=(a-5b)(a-5b+1)-6(a-5b+1)
=(a-5b+1)(a-5b-6)

3.(C) 4.(D)

Answer 2

1. (分组后可直接提公因式)
(分组后可运用公式)
(分组后既可提公因式又可运用公式)
2. x＾2-xy-2y＾2-x-y
=(x＾2-y＾2)-(xy+y＾2)-(x+y)
=(x+y)(x-y)-y(x+y)-(x+y)
=(x+y)(x-y-y-1)
=(x+y)(x-2y-1)

x＾3+2x＾2-5x-6
=(x＾3+2x＾2+x)-(6x+6)
=x(x+1)＾2-6(x+1)
=(x+1)(x＾2+x-6)
=(x+1)[(x＾2+3x)-(2x+6)]
=(x+1)[x(x+3)-2(x+3)]
=(x+1)(x+3)(x-2)

a＾2-6ab+9b＾2-4a+12b+4
=(a＾2-6ab+9b＾2)-(4a-12b)+4
=(a-3b)＾2-4(a-3b)+4
=(a-3b-2)＾2

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

a＾2-10ab+25b＾2-5a+25b-6
=(a＾2-10ab+25b＾2)-(5a-25b)-6
=(a-5b)＾2-[(6a-30b)-(a-5b)]-6
=[(a-5b)＾2+(a-5b)]-6[(a-5b)+1]
=(a-5b)(a-5b+1)-6(a-5b+1)
=(a-5b+1)(a-5b-6)

3.(C) 4.(D)

Answer 3

1. (分组后可直接提公因式)
(分组后可运用公式)
(分组后既可提公因式又可运用公式)
2. x＾2-xy-2y＾2-x-y
=(x＾2-y＾2)-(xy+y＾2)-(x+y)
=(x+y)(x-y)-y(x+y)-(x+y)
=(x+y)(x-y-y-1)
=(x+y)(x-2y-1)

x＾3+2x＾2-5x-6
=(x＾3+2x＾2+x)-(6x+6)
=x(x+1)＾2-6(x+1)
=(x+1)(x＾2+x-6)
=(x+1)[(x＾2+3x)-(2x+6)]
=(x+1)[x(x+3)-2(x+3)]
=(x+1)(x+3)(x-2)

a＾2-6ab+9b＾2-4a+12b+4
=(a＾2-6ab+9b＾2)-(4a-12b)+4
=(a-3b)＾2-4(a-3b)+4
=(a-3b-2)＾2

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

a＾2-10ab+25b＾2-5a+25b-6
=(a＾2-10ab+25b＾2)-(5a-25b)-6
=(a-5b)＾2-[(6a-30b)-(a-5b)]-6
=[(a-5b)＾2+(a-5b)]-6[(a-5b)+1]
=(a-5b)(a-5b+1)-6(a-5b+1)
=(a-5b+1)(a-5b-6)

3.(C) 4.(D)

参考资料：谢谢楼上的楼上的朋友.