展开 (5x^3-e^{4x})^2

解答

展开

(5 x^{3} - e^{4 x})^{2}

25 x^{6} - 10 e^{4 x} x^{3} + e^{8 x}

求解步骤

(5 x^{3} - e^{4 x})^{2}

使用完全平方公式:

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

a = 5 x^{3}, b = e^{4 x}

= (5 x^{3})^{2} - 2 \cdot 5 x^{3} e^{4 x} + (e^{4 x})^{2}

化简

(5 x^{3})^{2} - 2 \cdot 5 x^{3} e^{4 x} + (e^{4 x})^{2} : 25 x^{6} - 10 e^{4 x} x^{3} + e^{8 x}

= 25 x^{6} - 10 e^{4 x} x^{3} + e^{8 x}

e x p an d 2 \cdot 1.97 \cdot (1, 7 - 0)

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

e x p an d \frac{4 ( x + 2 ) ( x - 1 )}{( x ^{2} + 2 x + 2 ) ^{2}}

e x p an d \frac{8}{s ^{3} ( s ^{2} - s - 2 )}

e x p an d \frac{x}{( x ^{2} + 4 ) ( x - 3 )}