What is expand (x-iy)^3 ?

The solution to expand (x-iy)^3 is (x^3-3xy^2)+(-3x^2y+y^3)i

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expand (x-iy)^3

expand

(x - i y)^{3}

(x^{3} - 3 x y^{2}) + (- 3 x^{2} y + y^{3}) i

Solution steps

(x - i y)^{3}

Apply Perfect Cube Formula:

(a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3}

(x - i y)^{3} = x^{3} - 3 x^{2} i y + 3 x (i y)^{2} - (i y)^{3}

= x^{3} - 3 x^{2} i y + 3 x (i y)^{2} - (i y)^{3}

Simplify

x^{3} - 3 x^{2} i y + 3 x (i y)^{2} - (i y)^{3} : x^{3} - 3 x^{2} y i - 3 x y^{2} + i y^{3}

= x^{3} - 3 x^{2} y i - 3 x y^{2} + i y^{3}

Rewrite in standard complex form:

(x^{3} - 3 x y^{2}) + (- 3 x^{2} y + y^{3}) i

= (x^{3} - 3 x y^{2}) + (- 3 x^{2} y + y^{3}) i

2 \times 13

+ 6 x - x^{2} - 8

+ \frac{27 e ^{7}}{3 e ^{4}}

\frac{4}{6} - \frac{5}{8}

What is expand (x-iy)^3 ?
The solution to expand (x-iy)^3 is (x^3-3xy^2)+(-3x^2y+y^3)i