What is expand [x-(4i-2)][x-(4i+2)](x-2) ?

The solution to expand [x-(4i-2)][x-(4i+2)](x-2) is (x^3-2x^2-20x+40)+(-8x^2+16x)i

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expand [x-(4i-2)][x-(4i+2)](x-2)

expand

[x - (4 i - 2)] [x - (4 i + 2)] (x - 2)

(x^{3} - 2 x^{2} - 20 x + 40) + (- 8 x^{2} + 16 x) i

Solution steps

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

Expand

(x - (4 i - 2)) (x - (4 i + 2)) (x - 2) : (x^{2} - 8 x i - 20) (x - 2)

= (x^{2} - 8 x i - 20) (x - 2)

Distribute parentheses

= x^{2} x + x^{2} (- 2) - 8 x i x - 8 x i (- 2) - 20 x - 20 (- 2)

Simplify

x^{2} x + x^{2} (- 2) - 8 x i x - 8 x i (- 2) - 20 x - 20 (- 2) : x^{3} - 2 x^{2} - 8 x^{2} i + 16 x i - 20 x + 40

= x^{3} - 2 x^{2} - 8 x^{2} i + 16 x i - 20 x + 40

Rewrite in standard complex form:

(x^{3} - 2 x^{2} - 20 x + 40) + (- 8 x^{2} + 16 x) i

= (x^{3} - 2 x^{2} - 20 x + 40) + (- 8 x^{2} + 16 x) i

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

\frac{27 e ^{x} - 3 e ^{3 x}}{( 3 + e ^{x} ) ^{4}}

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

(x + 2 - 3) \cdot (x + 2 + 3)

2 (2 + 3)

What is expand [x-(4i-2)][x-(4i+2)](x-2) ?
The solution to expand [x-(4i-2)][x-(4i+2)](x-2) is (x^3-2x^2-20x+40)+(-8x^2+16x)i