证明：(x-1)(x-3)(x-5)(x-7)+16是完全平方式
问题描述：
证明：(x-1)(x-3)(x-5)(x-7)+16是完全平方式
答
原式=(x-1)(x-3)(x-5)(x-7)+16
=(x-1)(x-7)(x-3)(x-5)+16
=(x^2-8x+7)（x^2-8x+15）+16
=[(x^2-8x)+7][（x^2-8x）+15]+16
=(x^2-8x）^2+22(x^2-8x)+105+16
=(x^2-8x）^2+22(x^2-8x)+121
=(x^2-8x）^2+2×11(x^2-8x)+11^2
=(x^2-8x+11)^2
得证!