展开 (3z-2y)^3

解答

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(3 z - 2 y)^{3}

27 z^{3} - 54 z^{2} y + 36 z y^{2} - 8 y^{3}

求解步骤

(3 z - 2 y)^{3}

使用完全立方公式:

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

(3 z - 2 y)^{3} = (3 z)^{3} - 3 (3 z)^{2} \cdot 2 y + 3 \cdot 3 z (2 y)^{2} - (2 y)^{3}

= (3 z)^{3} - 3 (3 z)^{2} \cdot 2 y + 3 \cdot 3 z (2 y)^{2} - (2 y)^{3}

化简

(3 z)^{3} - 3 (3 z)^{2} \cdot 2 y + 3 \cdot 3 z (2 y)^{2} - (2 y)^{3} : 27 z^{3} - 54 z^{2} y + 36 z y^{2} - 8 y^{3}

= 27 z^{3} - 54 z^{2} y + 36 z y^{2} - 8 y^{3}

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