simplify (x-3i)^3

Solution

simplify

(x - 3 i)^{3}

(x^{3} - 27 x) + (- 9 x^{2} + 27) i

Solution steps

(x - 3 i)^{3}

Apply Perfect Cube Formula:

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

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

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

Simplify

x^{3} - 3 x^{2} \cdot 3 i + 3 x (3 i)^{2} - (3 i)^{3} : x^{3} - 9 x^{2} i - 27 x + 27 i

= x^{3} - 9 x^{2} i - 27 x + 27 i

Rewrite in standard complex form:

(x^{3} - 27 x) + (- 9 x^{2} + 27) i

= (x^{3} - 27 x) + (- 9 x^{2} + 27) i

x^{\frac{4}{5}} (x - 9)^{2}

\frac{x ^{2} - x - 2}{( x - 3 ) ^{2}}

A (1, 3) y B (- 2, - 7)

\frac{x}{( x + 2 ) ( x - 3 )}

(2 x + 1) (2 x + 1)