1.(m-1)^2-4(n-1)^22.-9+81x^23.4(2x-y)-(x+y)^24.(a-b)^3+4ab(a-b)第三题改为4（2x-y）^2-(x+y)^2

Question

1.(m-1)^2-4(n-1)^2
2.-9+81x^2
3.4(2x-y)-(x+y)^2
4.(a-b)^3+4ab(a-b)
第三题改为4（2x-y）^2-(x+y)^2

Answer 1

1.
(m-1)^2-4(n-1)^2
=[(m-1)-2(n-1)][(m-1)+2(n-1)]
=(m-1-2n+2)(m-1+2n-2)
=(m-2n+1)(m+2n-3)
2.
-9+81x^2
=9(-1+9x^2)
=9(3x-1)(3x+1)
3.
4(2x-y)^2-(x+y)^2
=[2(2x-y)]^2-(x+y)^2
=[2(2x-y)-(x+y)][2(2x-y)+(x+y)]
=(4x-2y-x-y)(4x-2y+x+y)
=(3x-3y)(5x-y)
=3(x-y)(5x-y)
4.
(a-b)^3+4ab(a-b)
=(a-b)[(a-b)^2+4ab]
=(a-b)(a^2+b^2-2ab+4ab)
=(a-b)(a^2+b^2+2ab)
=(a-b)(a+b)^2