展开 (4e-3f)^3

解答

展开

(4 e - 3 f)^{3}

- 27 f^{3} + 108 e f^{2} - 144 e^{2} f + 64 e^{3}

求解步骤

(4 e - 3 f)^{3}

使用完全立方公式:

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

a = 4 e, b = 3 f

= (4 e)^{3} - 3 (4 e)^{2} \cdot 3 f + 3 \cdot 4 e (3 f)^{2} - (3 f)^{3}

化简

(4 e)^{3} - 3 (4 e)^{2} \cdot 3 f + 3 \cdot 4 e (3 f)^{2} - (3 f)^{3} : 64 e^{3} - 144 e^{2} f + 108 e f^{2} - 27 f^{3}

= 64 e^{3} - 144 e^{2} f + 108 e f^{2} - 27 f^{3}

改写为标准形式

= - 27 f^{3} + 108 e f^{2} - 144 e^{2} f + 64 e^{3}

e x p an d (2 e^{3 x} + e^{- 3 x})^{2}

e x p an d \frac{( x + 2 ) ( x - 3 )}{( x - 2 ) ( x + 5 )}

e x p an d \frac{( 1 - cos ( x ) ) ^{2}}{x}

e x p an d \frac{3 x + 5}{( x - 1 ) ( x ^{4} + 7 )}

e x p an d (x + b x)^{2} + 25