Factorization 8a-4a^-4 9(x+y)^-81(x-y)^ 4b^c^-(b^+c^-a^)^ Proof: the square difference of any two odd numbers is a multiple of 8

Factorization 8a-4a^-4 9(x+y)^-81(x-y)^ 4b^c^-(b^+c^-a^)^ Proof: the square difference of any two odd numbers is a multiple of 8

1.8a-4a^-4= -4(a^-2a+1)=-4(a-1)^
2.9(x+y)^-81(x-y)^ =[3(x+y)]^-[9(x-y)]^
=(3x+3y+9x-9y)(3x+3y-9x+9y)=(12x-6y)(12y-6x)=36(2x-y)(2y-x)
3.4b^c^-(b^+c^-a^)^ =(2bc)^-(b^+c^-a^)^
=(2bc+b^+c^-a^)(2bc-b^-c^+a^)=[(b+c)^-a^][a^-(b-x)^]
=(b+c+a)(b+c-a)(a+b-c)(a-b+c)
4. (2n + 1) ^ - (2n-1) ^ = 4N * 2 = 8N, so it is a multiple of 8