几道数学填空题1.(a-b+c-d)^2-(a+b-c+d)^2=2.(x-3y)(x+3y)(x^2-9y^2)=3.(x-y-m+n)(x+y-m-n)=4.(a-b)(a+b)^3-2ab(a^2-b^2)=5.(m-n)=n^2-m^26.(2a-b+3c)^2=

Question

几道数学填空题
1.(a-b+c-d)^2-(a+b-c+d)^2=
2.(x-3y)(x+3y)(x^2-9y^2)=
3.(x-y-m+n)(x+y-m-n)=
4.(a-b)(a+b)^3-2ab(a^2-b^2)=
5.(m-n) =n^2-m^2
6.(2a-b+3c)^2=

Answer 1

1.(a-b+c-d)^2-(a+b-c+d)^2
=[(a-b+c-d)+(a+b-c+d)][(a-b+c-d)-(a+b-c+d)]
=(2a)*(-2b+2c-2d)
=-4ab+4ac-4ad
2.(x-3y)(x+3y)(x^2-9y^2)
=(x^2-9y^2)(x^2-9y^2)
=(x^2-9y^2)^2
=x^4-18x^2y^2+81y^2
3.(x-y-m+n)(x+y-m-n)
=[(x-m)-(y-n)][(x-m)+(y-n)]
=(x-m)^2-(y-n)^2
=x^2-2mx+m^2-y^2+2ny-n^2
4.(a-b)(a+b)^3-2ab(a^2-b^2)
=(a-b)(a+b)(a+b)^2-2ab(a^2-b^2)
=(a^2-b^2)(a+b)^2-2ab(a^2-b^2)
=(a^2-b^2)[(a+b)^2-2ab]
=(a^2-b^2)(a^2+b^2)
=a^4-b^4
5.(m-n)=n^2-m^2?
应该是
(m-n)^2+n^2-m^2
=m^2-2mn+n^2+n^2-m^2
=2n^2-2mn
6.(2a-b+3c)^2
=4a^2+b^2+9c^2-4ab+12ac-6bc