해법
요인 (x+b+1)6+(z+c−1)6
해법
(x2+2bx+2x+b2+2b+c2+2cz+z2+2−2c−2z)(x4+4bx3+4x3+6b2x2+12bx2+2cx2+2x2z+5x2−c2x2−x2z2−2cx2z+4b3x+12b2x+10bx+4bcx+4cx+4bxz+4xz+2x−2bc2x−2c2x−2bxz2−2xz2−4bcxz−4cxz+b4+4b3+5b2+2b2c+2b2z+2b+4bc+4bz+c4+4c3z+5c2+6c2z2+4cz3+10cz+z4+5z2+1−b2c2−b2z2−2b2cz−2bc2−2bz2−4bcz−4c3−12c2z−2c−12cz2−4z3−2z)
솔루션 단계
(x+b+1)6+(z+c−1)6
(x+b+1)6+(z+c−1)6((x+b+1)2)3+((z+c−1)2)3 로 다시 씁니다
=((x+b+1)2)3+((z+c−1)2)3
입방체의 합 공식 적용: x3+y3=(x+y)(x2−xy+y2)((x+b+1)2)3+((z+c−1)2)3=((x+b+1)2+(z+c−1)2)((x+b+1)4−(x+b+1)2(z+c−1)2+(z+c−1)4)=((x+b+1)2+(z+c−1)2)((x+b+1)4−(x+b+1)2(z+c−1)2+(z+c−1)4)
(x+b+1)2+(z+c−1)2확대한다:x2+2bx+2x+b2+2b+c2+2cz+z2+2−2c−2z
=(x2+2bx+2x+b2+2b+c2+2cz+z2+2−2c−2z)((x+b+1)4−(x+b+1)2(z+c−1)2+(z+c−1)4)
(x+b+1)4−(x+b+1)2(z+c−1)2+(z+c−1)4확대한다:x4+4bx3+4x3+6b2x2+12bx2+2cx2+2x2z+5x2−c2x2−x2z2−2cx2z+4b3x+12b2x+10bx+4bcx+4cx+4bxz+4xz+2x−2bc2x−2c2x−2bxz2−2xz2−4bcxz−4cxz+b4+4b3+5b2+2b2c+2b2z+2b+4bc+4bz+c4+4c3z+5c2+6c2z2+4cz3+10cz+z4+5z2+1−b2c2−b2z2−2b2cz−2bc2−2bz2−4bcz−4c3−12c2z−2c−12cz2−4z3−2z
=(x2+2bx+2x+b2+2b+c2+2cz+z2+2−2c−2z)(x4+4bx3+4x3+6b2x2+12bx2+2cx2+2x2z+5x2−c2x2−x2z2−2cx2z+4b3x+12b2x+10bx+4bcx+4cx+4bxz+4xz+2x−2bc2x−2c2x−2bxz2−2xz2−4bcxz−4cxz+b4+4b3+5b2+2b2c+2b2z+2b+4bc+4bz+c4+4c3z+5c2+6c2z2+4cz3+10cz+z4+5z2+1−b2c2−b2z2−2b2cz−2bc2−2bz2−4bcz−4c3−12c2z−2c−12cz2−4z3−2z)