展开 (x+pix)^3

解答

展开

(x + π x)^{3}

x^{3} + 3 π x^{3} + 3 π^{2} x^{3} + π^{3} x^{3}

求解步骤

(x + π x)^{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 = x, b = π x

= x^{3} + 3 x^{2} π x + 3 x (π x)^{2} + (π x)^{3}

化简

x^{3} + 3 x^{2} π x + 3 x (π x)^{2} + (π x)^{3} : x^{3} + 3 π x^{3} + 3 π^{2} x^{3} + π^{3} x^{3}

= x^{3} + 3 π x^{3} + 3 π^{2} x^{3} + π^{3} x^{3}

e x p an d (x^{3} + x y^{2} + a^{2} y) d x

e x p an d \frac{x + 77}{x ( x + 11 )}

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

e x p an d \frac{( n - 1 ) \cdot n}{2} + (n - 1)

e x p an d 1.124001 e + 21