解
展開する (ab(x−z)+y+c)3
解
a3b3(x−z)(x−z)(x−z)+a23b2x2y+3b2z2y+3b2x2c+3b2z2c−6xb2zy−2xb2cz−2cxb2z−2b2cxz+a3bxy2−3bzy2+3bxc2−3bzc2+6bcxy−6bczy+y3+3cy2+3yc2+c3
解答ステップ
(ab(x−z)+y+c)3
簡素化 (ab(x−z)+y+c)3:(ab(x−z)+y+c)(ab(x−z)+y+c)(ab(x−z)+y+c)
=(ab(x−z)+y+c)(ab(x−z)+y+c)(ab(x−z)+y+c)
拡張 (ab(x−z)+y+c)(ab(x−z)+y+c):a2b2(x−z)(x−z)+a2bxy−2bzy+2bcx−2bcz+y2+2cy+c2
=(a2b2(x−z)(x−z)+a2bxy−2bzy+2bcx−2bcz+y2+2cy+c2)(ab(x−z)+y+c)
括弧を分配する=a2b2(x−z)(x−z)⋅ab(x−z)+a2b2(x−z)(x−z)y+a2b2(x−z)(x−z)c+a2bxy−2bzy+2bcx−2bcz⋅ab(x−z)+a2bxy−2bzy+2bcx−2bczy+a2bxy−2bzy+2bcx−2bczc+y2ab(x−z)+y2y+y2c+2cyab(x−z)+2cyy+2cyc+c2ab(x−z)+c2y+c2c
簡素化 a2b2(x−z)(x−z)⋅ab(x−z)+a2b2(x−z)(x−z)y+a2b2(x−z)(x−z)c+a2bxy−2bzy+2bcx−2bcz⋅ab(x−z)+a2bxy−2bzy+2bcx−2bczy+a2bxy−2bzy+2bcx−2bczc+y2ab(x−z)+y2y+y2c+2cyab(x−z)+2cyy+2cyc+c2ab(x−z)+c2y+c2c:a3b3(x−z)(x−z)(x−z)+a23b2x2y+3b2z2y+3b2x2c+3b2z2c−6xb2zy−2xb2cz−2cxb2z−2b2cxz+a3bxy2−3bzy2+3bxc2−3bzc2+6bcxy−6bczy+y3+3cy2+3yc2+c3
=a3b3(x−z)(x−z)(x−z)+a23b2x2y+3b2z2y+3b2x2c+3b2z2c−6xb2zy−2xb2cz−2cxb2z−2b2cxz+a3bxy2−3bzy2+3bxc2−3bzc2+6bcxy−6bczy+y3+3cy2+3yc2+c3