simplify (x-2i)^3

Solution

simplify

(x - 2 i)^{3}

(x^{3} - 12 x) + (- 6 x^{2} + 8) i

Solution steps

(x - 2 i)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

x^{3} - 3 x^{2} \cdot 2 i + 3 x (2 i)^{2} - (2 i)^{3} : x^{3} - 6 x^{2} i - 12 x + 8 i

= x^{3} - 6 x^{2} i - 12 x + 8 i

Rewrite in standard complex form:

(x^{3} - 12 x) + (- 6 x^{2} + 8) i

= (x^{3} - 12 x) + (- 6 x^{2} + 8) i

\frac{x}{s ^{2} ( s + 1 )}

(2 x^{2} t - 2 x^{3}) d t + (4 x^{3} - 6 x^{2} t + 2 x t^{2}) d x

\frac{e ^{- 3 s} ( 9 s ^{2} + 2 ( 3 s + 1 ) )}{s ^{3}}

f (x) (5 - x) e^{x}

\frac{x ( 2 x + 1 ) ( x - 5 )}{( x + 3 ) ( 3 x - 4 )}