What is expand (x+pix)^3 ?

The solution to expand (x+pix)^3 is x^3+3pix^3+3pi^2x^3+pi^3x^3

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expand (x+pix)^3

expand

(x + π x)^{3}

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

Solution steps

(x + π x)^{3}

Apply Perfect Cube Formula:

(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}

Simplify

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}

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

\frac{x + 77}{x ( x + 11 )}

\frac{z ^{2} + 1}{z ( z + 1 )}

\frac{( n - 1 ) \cdot n}{2} + (n - 1)

1.124001 e + 21

What is expand (x+pix)^3 ?
The solution to expand (x+pix)^3 is x^3+3pix^3+3pi^2x^3+pi^3x^3