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受欢迎的代数 >

因式分解 m^9-27n^{12}

解答

因式分解

m^{9} - 27 n^{12}

解答

(m^{3} - 3 n^{4}) (m^{6} + 3 m^{3} n^{4} + 9 n^{8})

求解步骤

m^{9} - 27 n^{12}

使用指数运算法则

= (m^{3})^{3} - (3 n^{4})^{3}

使用立方差公式:

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

(m^{3})^{3} - (3 n^{4})^{3} = (m^{3} - 3 n^{4}) ((m^{3})^{2} + m^{3} \cdot 3 n^{4} + (3 n^{4})^{2})

= (m^{3} - 3 n^{4}) ((m^{3})^{2} + m^{3} \cdot 3 n^{4} + (3 n^{4})^{2})

化简

(m^{3})^{2} + m^{3} \cdot 3 n^{4} + (3 n^{4})^{2} : m^{6} + 3 m^{3} n^{4} + 9 n^{8}

= (m^{3} - 3 n^{4}) (m^{6} + 3 m^{3} n^{4} + 9 n^{8})

流行的例子

x*(100-(1/((0.01)*(1.01)^{240)}))=240000

x \cdot (100 - (\frac{1}{( 0.01 ) \cdot ( 1.01 ) ^{240}})) = 240000

2 x + 9 + 3 x + x = 6 x + 9

(3 \cdot 5)^{6}

\frac{x}{4} - 8 \leq - 42

因式分解 2x^2+2x-4

f a c t or 2 x^{2} + 2 x - 4