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

The solution to (x+2i)^2(x-2i)^2 is x^4+8x^2+16

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

simplify

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

x^{4} + 8 x^{2} + 16

Solution steps

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

Expand

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

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

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

Expand

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

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

Distribute parentheses

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

Simplify

x^{2} x^{2} + x^{2} \cdot 4 x i + x^{2} (- 4) - 4 x i x^{2} - 4 x i 4 x i - 4 x i (- 4) - 4 x^{2} - 4 \cdot 4 x i - 4 (- 4) : x^{4} + 8 x^{2} + 16

= x^{4} + 8 x^{2} + 16

\frac{2 a ^{2} b}{b ^{2} c} \cdot \frac{b}{a}

x^{3} y^{3} + 64

\frac{\frac{3 π}{4}}{2}

lo g_{2} (2^{3})

36 m^{2} - 121