展开 a(e+2d)^3+b(e+2d)^3+c

解答

展开

a (e + 2 d)^{3} + b (e + 2 d)^{3} + c

e^{3} a + 6 e^{2} a d + 12 e a d^{2} + 8 a d^{3} + e^{3} b + 6 e^{2} d b + 12 e d^{2} b + 8 d^{3} b + c

求解步骤

a (e + 2 d)^{3} + b (e + 2 d)^{3} + c

(e + 2 d)^{3} = e^{3} + 6 e^{2} d + 12 e d^{2} + 8 d^{3}

= a (8 d^{3} + 12 e d^{2} + 6 e^{2} d + e^{3}) + b (2 d + e)^{3} + c

(e + 2 d)^{3} = e^{3} + 6 e^{2} d + 12 e d^{2} + 8 d^{3}

= a (8 d^{3} + 12 e d^{2} + 6 e^{2} d + e^{3}) + b (8 d^{3} + 12 e d^{2} + 6 e^{2} d + e^{3}) + c

乘开

a (e^{3} + 6 e^{2} d + 12 e d^{2} + 8 d^{3}) : e^{3} a + 6 e^{2} a d + 12 e a d^{2} + 8 a d^{3}

= e^{3} a + 6 e^{2} a d + 12 e a d^{2} + 8 a d^{3} + b (e^{3} + 6 e^{2} d + 12 e d^{2} + 8 d^{3}) + c

乘开

b (e^{3} + 6 e^{2} d + 12 e d^{2} + 8 d^{3}) : e^{3} b + 6 e^{2} d b + 12 e d^{2} b + 8 d^{3} b

= e^{3} a + 6 e^{2} a d + 12 e a d^{2} + 8 a d^{3} + e^{3} b + 6 e^{2} d b + 12 e d^{2} b + 8 d^{3} b + c

e x p an d (e + c + f)^{2}

e x p an d (3 x + \frac{\frac{7}{8}}{x})^{8}

e x p an d (m u cos (θ) + n u cos (θ) - m v)^{2}

e x p an d \frac{7}{( s + 3 ) ^{3}}

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