展开 sin^3(2x)(5x+3)^7

解答

展开

sin^{3} (2 x) (5 x + 3)^{7}

78125 sin^{3} (2 x) x^{7} + 328125 sin^{3} (2 x) x^{6} + 590625 sin^{3} (2 x) x^{5} + 590625 sin^{3} (2 x) x^{4} + 354375 sin^{3} (2 x) x^{3} + 127575 sin^{3} (2 x) x^{2} + 25515 x sin^{3} (2 x) + 2187 sin^{3} (2 x)

求解步骤

sin^{3} (2 x) (5 x + 3)^{7}

展开

(5 x + 3)^{7} : 78125 x^{7} + 328125 x^{6} + 590625 x^{5} + 590625 x^{4} + 354375 x^{3} + 127575 x^{2} + 25515 x + 2187

= sin^{3} (2 x) (78125 x^{7} + 328125 x^{6} + 590625 x^{5} + 590625 x^{4} + 354375 x^{3} + 127575 x^{2} + 25515 x + 2187)

打开括号

= sin^{3} (2 x) \cdot 78125 x^{7} + sin^{3} (2 x) \cdot 328125 x^{6} + sin^{3} (2 x) \cdot 590625 x^{5} + sin^{3} (2 x) \cdot 590625 x^{4} + sin^{3} (2 x) \cdot 354375 x^{3} + sin^{3} (2 x) \cdot 127575 x^{2} + sin^{3} (2 x) \cdot 25515 x + sin^{3} (2 x) \cdot 2187

= 78125 sin^{3} (2 x) x^{7} + 328125 sin^{3} (2 x) x^{6} + 590625 sin^{3} (2 x) x^{5} + 590625 sin^{3} (2 x) x^{4} + 354375 sin^{3} (2 x) x^{3} + 127575 sin^{3} (2 x) x^{2} + 25515 x sin^{3} (2 x) + 2187 sin^{3} (2 x)

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

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

e x p an d (x - \frac{1}{2})^{2} - \frac{81}{4}

e x p an d \frac{( 5 a - 2 b ) ( 3 ab )}{2}

s im pl i f y 3 (1 - cos (t))