(x-1)(x-3)(x+5)(x+7)+63 分解因式

(x-1)(x-3)(x+5)(x+7)+63

=(x-1)(x+5)(x-3)(x+7)+63

=(x^2+4x-5)(x^2+4x-21)+63

=(x^2+4x-5)^2-16(x^2+4x-5)+63

=(x^2+4x-5-7)(x^2+4x-5-9)

=(x^2+4x-12)(x^2+4x-14)

=(x+6)(x-2)(x^2+4x-14)

(x-1)(x-3)(x+1+4)(x+3+4)+63=(x^2+4x-3)(x^2+4x-11)+63=x^4+8x^3+2x^2-56x+96

(x-1)(x-3)(x+5)(x+7)+63
=(x-1)(x+5)(x-3)(x+7)+63------------------乘法交换律
=(x^2+4x-5)(x^2+4x-21)+63-----------------整式乘法
=(x^2+4x-5)^2-16(x^2+4x-5)+63-----------------拆项
=(x^2+4x-5-7)(x^2+4x-5-9)----------------------因式分解
=(x^2+4x-12)(x^2+4x-14)-----------------------合并同类项
=(x+6)(x-2)(x^2+4x-14) -------------------再次因式分解

(x-1)(x-3)(x+5)(x+7)+63
=(x-1)(x+5)(x-3)(x+7)+63
=(x^2+4x-5)(x^2+4x-21)+63
=(x^2+4x)^2-26(x^2+4x)+105+63
=(x^2+4x)^2-26(x^2+4x)+168
=[(x^2+4x)-12][(x^2+4x)+14]
=(x^2+4x-12)(x^2+4x+14)
=(x+6)(x-2)(x^2+4x+14)