展开 4(3e^{3x}+2cos(2x))^3

解答

展开

4 (3 e^{3 x} + 2 cos (2 x))^{3}

108 e^{9 x} + 216 e^{6 x} cos (2 x) + 144 e^{3 x} cos^{2} (2 x) + 32 cos^{3} (2 x)

求解步骤

4 (3 e^{3 x} + 2 cos (2 x))^{3}

(3 e^{3 x} + 2 cos (2 x))^{3} = 27 e^{9 x} + 54 e^{6 x} cos (2 x) + 36 e^{3 x} cos^{2} (2 x) + 8 cos^{3} (2 x)

= 4 (27 e^{9 x} + 8 cos^{3} (2 x) + 36 e^{3 x} cos^{2} (2 x) + 54 e^{6 x} cos (2 x))

打开括号

= 4 \cdot 27 e^{9 x} + 4 \cdot 54 e^{6 x} cos (2 x) + 4 \cdot 36 e^{3 x} cos^{2} (2 x) + 4 \cdot 8 cos^{3} (2 x)

化简

4 \cdot 27 e^{9 x} + 4 \cdot 54 e^{6 x} cos (2 x) + 4 \cdot 36 e^{3 x} cos^{2} (2 x) + 4 \cdot 8 cos^{3} (2 x) : 108 e^{9 x} + 216 e^{6 x} cos (2 x) + 144 e^{3 x} cos^{2} (2 x) + 32 cos^{3} (2 x)

= 108 e^{9 x} + 216 e^{6 x} cos (2 x) + 144 e^{3 x} cos^{2} (2 x) + 32 cos^{3} (2 x)

e x p an d \frac{20}{s ( s + 1 ) ( 0.5 s + 1 )}

e x p an d 1 + x^{2} d y + (x + y + 1 + x^{2}) d x

e x p an d \frac{d ^{2}}{d ^{2} x} (x y + 5 e^{y} = 5 e)

e x p an d \frac{4.5805 ( z - 0.4776 )}{( z )}

s im pl i f y 40 (2 - 2)