Question

分解因式 m(x+y)^2-m(x+y)-2m

x^4-7x^2y^2+6y^4
(a-b)^3+6(b-a)^2-5(b-a)
(m+n)^2-4k(zm+n)+3k^2
(a-b)^2-12(a-b)-45
(a+b)^2+m(a+b)-12m^ 2
m(x+y)^2-m(x+y)-2m

(m+n)^2-4k(2m+n)+3k^2
是2不是z
谢谢

Answer 1

1.m(x+y)^2-m(x+y)-2m
=m[(x+y)^2-(x+y)-2]
=m(x+y+1)(x+y-2);
2.x^4-7x^2y^2+6y^4
=(x^2-6y^2)(x^2-y^2)
=(x^2-6y^2)(x+y)(x-y);
3.(a-b)^3+6(b-a)^2-5(b-a)
=(a-b)[(a-b)^2+6(a-b)+5]
=(a-b)(a-b+1)^(a-b+5);
4.(m+n)^2-4k(zm+n)+3k^2
=(m+n-k)(m+n-3k);
5.(a-b)^2-12(a-b)-45
=(a-b-15)(a-b+3)
6.(a+b)^2+m(a+b)-12m^ 2
=(a+b+4m)(a+b-3m).
补1.（x^2-4x^2-9x^2-4x)-20
=.-12^2-4x-20
=-4(3x^2+x+5);
2.(x^2-2x)^2-7(x^2-2x)-8
=(x^2-2x-8)(x^2-2x+1)
=(x-4)(x+2)(x-1)^2;
3.(a^2+5a+3)(a^2+5a-2)-6
=.(a^2+5a)^2+(a^2+5a)-6-6
=.(a^2+5a+4)(a^2+5a-3)
=.(a+1)(a+4)(a^2+5a-3);
4.x^2+4xy+4y^2+4x+8y+3
=(x+2y)^2+2(x+2y)+3
=...
5.(x+3)(x^2-1)(x+5)-20
=展开后再分解
6.a^2-2a+b^2-2b+2ab+1
=a^2+2ab+b^2-2a-2b+1
=同补4方法
7.(x^2+3x+2)(4x^2+8x+3)-90
=展开后再分解
8.(x+1)(x+2)(x+3)(x+6)+x^2
=展开后再分解
9.(x-2)^3-(y-2)^3-(x-y)^3
=（x-y)[(x-2)^2+(x-2)(y-2)+(y-2)^2]-(x-y)^3
=(x-y)[(x^2+xy+y^2)-6(x+y)+12]-(x-y)^3
=-6(x-y)(x+y-2)
10.(2x^2-3x+1)^2-22x^2+33x-1
=(2x^2-3x+1)^2-11(2x^2+3x+1)+11-1
=(2x^2-3x+1-1)(2x^2-3x+1-10)
=继续因式分解

希望对你有用！

Answer 2

x^4-7x^2y^2+6y^4
=(x²-6y²)(x²-y²)
=(x²-6y²)(x+y)(x-y)

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

(m+n)^2-4k(zm+n)+3k^2
=?/
写错了，不应该有z

(m+n)^2-4k(m+n)+3k^2
=(m+n-3k)(m+n-k)

(a-b)^2-12(a-b)-45
=(a-b-15)(a-b+3)

(a+b)^2+m(a+b)-12m^ 2
=(a+b+4m)(a+b-3m)

Answer 3

x^4-7x^2y^2+6y^4 =（x^2-y^2）(x^2-6y^2)
(a-b)^3+6(b-a)^2-5(b-a) =(a-b)(a-b+1)(a-b+5)
(m+n)^2-4k(zm+n)+3k^2 =(m+n-k)(m+n-3k)
(a-b)^2-12(a-b)-45=(a-b-15)(a-b+3)
a+b)^2+m(a+b)-12m^ 2=(a+b-3m)(a+b+4m)