展开 (1+2e^t)^3

解答

展开

(1 + 2 e^{t})^{3}

1 + 6 e^{t} + 12 e^{2 t} + 8 e^{3 t}

求解步骤

(1 + 2 e^{t})^{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 = 1, b = 2 e^{t}

= 1^{3} + 3 \cdot 1^{2} \cdot 2 e^{t} + 3 \cdot 1 \cdot (2 e^{t})^{2} + (2 e^{t})^{3}

化简

1^{3} + 3 \cdot 1^{2} \cdot 2 e^{t} + 3 \cdot 1 \cdot (2 e^{t})^{2} + (2 e^{t})^{3} : 1 + 6 e^{t} + 12 e^{2 t} + 8 e^{3 t}

= 1 + 6 e^{t} + 12 e^{2 t} + 8 e^{3 t}

e x p an d (1 + \frac{x}{2})^{16}

e x p an d \frac{x ^{2} + 2 x - 3}{( x + 1 ) ^{2}}

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

e x p an d \frac{( 4 y ^{4} - 9 ) ^{2}}{144 y ^{4}}

s im pl i f y 2 (1 + 3)