What is (x+2i)(x-2i)^2 ?

The solution to (x+2i)(x-2i)^2 is (x^3+4x)+(-2x^2-8)i

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (x+2i)(x-2i)^2

simplify

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

(x^{3} + 4 x) + (- 2 x^{2} - 8) i

Solution steps

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

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

Expand

(x - 2 i)^{2} : x^{2} - 4 x i - 4

= (x^{2} - 4 x i - 4) (x + 2 i)

Distribute parentheses

= x^{2} x + x^{2} \cdot 2 i - 4 x i x - 4 x i 2 i - 4 x - 4 \cdot 2 i

Simplify

x^{2} x + x^{2} \cdot 2 i - 4 x i x - 4 x i 2 i - 4 x - 4 \cdot 2 i : x^{3} - 2 x^{2} i + 4 x - 8 i

= x^{3} - 2 x^{2} i + 4 x - 8 i

Rewrite in standard complex form:

(x^{3} + 4 x) + (- 2 x^{2} - 8) i

= (x^{3} + 4 x) + (- 2 x^{2} - 8) i

((x - 2) \cdot x) \cdot (72 + 7 x)

\frac{1}{( 1 + 2 x ) ^{3}}

(1 + \frac{1}{x})^{6}

\frac{x ^{3}}{2 ( x - 1 ) ^{2}}

(x^{3} e^{3 x} + 2) (x)