展开 ((2+2x)^4)/((1+xsqrt(3))^6)

解答

展开

\frac{( 2 + 2 x ) ^{4}}{( 1 + x 3 ) ^{6}}

\frac{16 + 64 x + 96 x ^{2} + 64 x ^{3} + 16 x ^{4}}{1 + 6 3 x + 45 x ^{2} + 60 3 x ^{3} + 135 x ^{4} + 54 3 x ^{5} + 27 x ^{6}}

求解步骤

\frac{( 2 + 2 x ) ^{4}}{( 1 + x 3 ) ^{6}}

(1 + x 3)^{6} = 1 + 63 x + 45 x^{2} + 603 x^{3} + 135 x^{4} + 543 x^{5} + 27 x^{6}

= \frac{( 2 + 2 x ) ^{4}}{1 + 6 3 x + 45 x ^{2} + 60 3 x ^{3} + 135 x ^{4} + 54 3 x ^{5} + 27 x ^{6}}

(2 + 2 x)^{4} = 16 + 64 x + 96 x^{2} + 64 x^{3} + 16 x^{4}

= \frac{16 + 64 x + 96 x ^{2} + 64 x ^{3} + 16 x ^{4}}{1 + 6 3 x + 45 x ^{2} + 60 3 x ^{3} + 135 x ^{4} + 54 3 x ^{5} + 27 x ^{6}}

e x p an d 6 a \cdot (5 - 3)

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

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

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

e x p an d tan (\frac{β}{2}) \cdot (1 + cos (β))