因式分解 (8x)^{(3)}-(4y)^{(3)}

解答

因式分解

(8 x)^{(3)} - (4 y)^{(3)}

64 (2 x - y) (4 x^{2} + 2 x y + y^{2})

求解步骤

(8 x)^{3} - (4 y)^{3}

使用立方差公式:

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

(8 x)^{3} - (4 y)^{3} = (8 x - 4 y) ((8 x)^{2} + 8 x 4 y + (4 y)^{2})

= (8 x - 4 y) ((8 x)^{2} + 8 x 4 y + (4 y)^{2})

化简

(8 x - 4 y) ((8 x)^{2} + 8 x \cdot 4 y + (4 y)^{2}) : (8 x - 4 y) (64 x^{2} + 32 x y + 16 y^{2})

= (8 x - 4 y) (64 x^{2} + 32 x y + 16 y^{2})

分解

(8 x - 4 y) (64 x^{2} + 32 x y + 16 y^{2}) : 64 (2 x - y) (4 x^{2} + 2 x y + y^{2})

= (8 x - 4 y) (64 x^{2} + 32 x y + 16 y^{2})

分解

8 x - 4 y : 4 (2 x - y)

= 4 (2 x - y) (64 x^{2} + 32 x y + 16 y^{2})

分解

64 x^{2} + 32 x y + 16 y^{2} : 16 (4 x^{2} + 2 x y + y^{2})

= 64 (2 x - y) (4 x^{2} + 2 x y + y^{2})

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