解
展開する (x−a)(x−b)(x−c)(x−d)(x−e)
解
x5−ex4−dx4+edx3−cx4+ecx3+cdx3−ecdx2−bx4+ebx3+bdx3−ebdx2+bcx3−ebcx2−bcdx2+ebcdx−ax4+eax3+adx3−eadx2+acx3−eacx2−acdx2+eacdx+abx3−eabx2−abdx2+eabdx−abcx2+eabcx+abcdx−eabcd
解答ステップ
(x−a)(x−b)(x−c)(x−d)(x−e)
拡張 (x−a)(x−b):x2−bx−ax+ab
=(x2−bx−ax+ab)(x−c)(x−d)(x−e)
拡張 (x2−bx−ax+ab)(x−c):x3−cx2−bx2+bcx−ax2+acx+abx−abc
=(x3−cx2−bx2+bcx−ax2+acx+abx−abc)(x−d)(x−e)
拡張 (x3−cx2−bx2+bcx−ax2+acx+abx−abc)(x−d):x4−dx3−cx3+cdx2−bx3+bdx2+bcx2−bcdx−ax3+adx2+acx2−acdx+abx2−abdx−abcx+abcd
=(x4−dx3−cx3+cdx2−bx3+bdx2+bcx2−bcdx−ax3+adx2+acx2−acdx+abx2−abdx−abcx+abcd)(x−e)
拡張 (x4−dx3−cx3+cdx2−bx3+bdx2+bcx2−bcdx−ax3+adx2+acx2−acdx+abx2−abdx−abcx+abcd)(x−e):x5−ex4−dx4+edx3−cx4+ecx3+cdx3−ecdx2−bx4+ebx3+bdx3−ebdx2+bcx3−ebcx2−bcdx2+ebcdx−ax4+eax3+adx3−eadx2+acx3−eacx2−acdx2+eacdx+abx3−eabx2−abdx2+eabdx−abcx2+eabcx+abcdx−eabcd
=x5−ex4−dx4+edx3−cx4+ecx3+cdx3−ecdx2−bx4+ebx3+bdx3−ebdx2+bcx3−ebcx2−bcdx2+ebcdx−ax4+eax3+adx3−eadx2+acx3−eacx2−acdx2+eacdx+abx3−eabx2−abdx2+eabdx−abcx2+eabcx+abcdx−eabcd