化简 (sqrt(6-3x^3)+6)^2

解答

化简

(6 - 3 x^{3} + 6)^{2}

- 3 x^{3} + 12 6 - 3 x^{3} + 42

求解步骤

(6 - 3 x^{3} + 6)^{2}

使用完全平方公式:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(6 - 3 x^{3} + 6)^{2} = (6 - 3 x^{3})^{2} + 2 6 - 3 x^{3} \cdot 6 + 6^{2}

= (6 - 3 x^{3})^{2} + 2 6 - 3 x^{3} \cdot 6 + 6^{2}

化简

(6 - 3 x^{3})^{2} + 2 6 - 3 x^{3} \cdot 6 + 6^{2} : - 3 x^{3} + 12 6 - 3 x^{3} + 42

= - 3 x^{3} + 12 6 - 3 x^{3} + 42

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