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

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

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

simplify

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

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

Solution steps

(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} (- 2 i) + 4 x i x + 4 x i (- 2 i) - 4 x - 4 (- 2 i)

Simplify

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

\frac{x}{( x + 1 ) ( x - 1 )}

e^{\frac{1}{3} (\frac{s ^{2}}{2} - 9 l n ∣ s ∣)}

2.8 tan (0.7 x - 1.8) - 2 (- 2, - 0.53)

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

\frac{2 x 1 + 6 x}{( x - 8 ) ^{2}}