簡約 a^2*(b+c)-(b+c)^3

解

簡約

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

a^{2} b + a^{2} c - b^{3} - 3 b^{2} c - 3 b c^{2} - c^{3}

解答ステップ

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

(b + c)^{3} : b^{3} + 3 b^{2} c + 3 b c^{2} + c^{3}

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

拡張

a^{2} (b + c) : a^{2} b + a^{2} c

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

- (b^{3} + 3 b^{2} c + 3 b c^{2} + c^{3}) : - b^{3} - 3 b^{2} c - 3 b c^{2} - c^{3}

= a^{2} b + a^{2} c - b^{3} - 3 b^{2} c - 3 b c^{2} - c^{3}