展開する (a^2-b^2)^3+(b^2-c^2)^3!(c^3-a^3)^3

解

展開する

(a^{2} - b^{2})^{3} + (b^{2} - c^{2})^{3}! (c^{3} - a^{3})^{3}

a^{6} - 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6} + c^{9} (b^{2} - c^{2})^{3}! - 3 c^{6} a^{3} (b^{2} - c^{2})^{3}! + 3 c^{3} a^{6} (b^{2} - c^{2})^{3}! - a^{9} (b^{2} - c^{2})^{3}!

解答ステップ

(a^{2} - b^{2})^{3} + (b^{2} - c^{2})^{3}! (c^{3} - a^{3})^{3}

拡張

(a^{2} - b^{2})^{3} : a^{6} - 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6}

= a^{6} - 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6} + (b^{2} - c^{2})^{3}! (c^{3} - a^{3})^{3}

拡張

(b^{2} - c^{2})^{3}! (c^{3} - a^{3})^{3} : c^{9} (b^{2} - c^{2})^{3}! - 3 c^{6} a^{3} (b^{2} - c^{2})^{3}! + 3 c^{3} a^{6} (b^{2} - c^{2})^{3}! - a^{9} (b^{2} - c^{2})^{3}!

= a^{6} - 3 a^{4} b^{2} + 3 a^{2} b^{4} - b^{6} + c^{9} (b^{2} - c^{2})^{3}! - 3 c^{6} a^{3} (b^{2} - c^{2})^{3}! + 3 c^{3} a^{6} (b^{2} - c^{2})^{3}! - a^{9} (b^{2} - c^{2})^{3}!