What is expand (x-5)(x-3+2i)(x-1-3i) ?

The solution to expand (x-5)(x-3+2i)(x-1-3i) is (x^3-9x^2+29x-45)+(-35+12x-x^2)i

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expand (x-5)(x-3+2i)(x-1-3i)

expand

(x - 5) (x - 3 + 2 i) (x - 1 - 3 i)

(x^{3} - 9 x^{2} + 29 x - 45) + (- 35 + 12 x - x^{2}) i

Solution steps

(x - 5) (x - 3 + 2 i) (x - 1 - 3 i)

Expand

(x - 5) (x - 3 + 2 i) : - 10 i + x^{2} - 8 x + 2 x i + 15

= (- 10 i + x^{2} - 8 x + 2 x i + 15) (x - 1 - 3 i)

Distribute parentheses

= - 10 i x - 10 i (- 1) - 10 i (- 3 i) + x^{2} x + x^{2} (- 1) + x^{2} (- 3 i) - 8 xx - 8 x (- 1) - 8 x (- 3 i) + 2 x i x + 2 x i (- 1) + 2 x i (- 3 i) + 15 x + 15 (- 1) + 15 (- 3 i)

Simplify

- 10 i x - 10 i (- 1) - 10 i (- 3 i) + x^{2} x + x^{2} (- 1) + x^{2} (- 3 i) - 8 xx - 8 x (- 1) - 8 x (- 3 i) + 2 x i x + 2 x i (- 1) + 2 x i (- 3 i) + 15 x + 15 (- 1) + 15 (- 3 i) : - 35 i + x^{3} - 9 x^{2} + 12 x i - x^{2} i + 29 x - 45

= - 35 i + x^{3} - 9 x^{2} + 12 x i - x^{2} i + 29 x - 45

Rewrite in standard complex form:

(x^{3} - 9 x^{2} + 29 x - 45) + (- 35 + 12 x - x^{2}) i

= (x^{3} - 9 x^{2} + 29 x - 45) + (- 35 + 12 x - x^{2}) i

\frac{s - 1}{( s - 2 ) ( s + 1 )}

\frac{2 ( m + 4 )}{m + 1}

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

\frac{p - 11}{( p - 1 ) ^{2}}

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

What is expand (x-5)(x-3+2i)(x-1-3i) ?
The solution to expand (x-5)(x-3+2i)(x-1-3i) is (x^3-9x^2+29x-45)+(-35+12x-x^2)i