因式分解 (9y^2)^3-(4z)^3

解答

因式分解

(9 y^{2})^{3} - (4 z)^{3}

(9 y^{2} - 4 z) (81 y^{4} + 36 y^{2} z + 16 z^{2})

求解步骤

(9 y^{2})^{3} - (4 z)^{3}

使用立方差公式:

x^{3} - y^{3} = (x - y) (x^{2} + x y + y^{2})

(9 y^{2})^{3} - (4 z)^{3} = (9 y^{2} - 4 z) ((9 y^{2})^{2} + 9 y^{2} 4 z + (4 z)^{2})

= (9 y^{2} - 4 z) ((9 y^{2})^{2} + 9 y^{2} 4 z + (4 z)^{2})

化简

(9 y^{2} - 4 z) ((9 y^{2})^{2} + 9 y^{2} \cdot 4 z + (4 z)^{2}) : (9 y^{2} - 4 z) (81 y^{4} + 36 y^{2} z + 16 z^{2})

= (9 y^{2} - 4 z) (81 y^{4} + 36 y^{2} z + 16 z^{2})

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