化简 (x-3i)^3

解答

化简

(x - 3 i)^{3}

(x^{3} - 27 x) + (- 9 x^{2} + 27) i

求解步骤

(x - 3 i)^{3}

使用完全立方公式:

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

(x - 3 i)^{3} = x^{3} - 3 x^{2} \cdot 3 i + 3 x (3 i)^{2} - (3 i)^{3}

= x^{3} - 3 x^{2} \cdot 3 i + 3 x (3 i)^{2} - (3 i)^{3}

化简

x^{3} - 3 x^{2} \cdot 3 i + 3 x (3 i)^{2} - (3 i)^{3} : x^{3} - 9 x^{2} i - 27 x + 27 i

= x^{3} - 9 x^{2} i - 27 x + 27 i

Rewrite in standard complex form:

(x^{3} - 27 x) + (- 9 x^{2} + 27) i

= (x^{3} - 27 x) + (- 9 x^{2} + 27) i

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