What is (x-13i)(x+5+10i)(x-5-10i) ?

The solution to (x-13i)(x+5+10i)(x-5-10i) is (x^3+75x-1300)+(-13x^2-100x-975)i

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simplify (x-13i)(x+5+10i)(x-5-10i)

simplify

(x - 13 i) (x + 5 + 10 i) (x - 5 - 10 i)

(x^{3} + 75 x - 1300) + (- 13 x^{2} - 100 x - 975) i

Solution steps

(x - 13 i) (x + 5 + 10 i) (x - 5 - 10 i)

Rewrite

x + 5 + 10 i

in standard complex form:

(x + 5) + 10 i

Rewrite

x - 5 - 10 i

in standard complex form:

(x - 5) - 10 i

= (x - 13 i) ((x + 5) + 10 i) ((x - 5) - 10 i)

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= ((x (x + 5) - (- 13) \cdot 10) + (x \cdot 10 - 13 (x + 5)) i) ((x - 5) - 10 i)

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= ((x (x + 5) - (- 13) \cdot 10) (x - 5) - (x \cdot 10 - 13 (x + 5)) (- 10)) + ((x (x + 5) - (- 13) \cdot 10) (- 10) + (x \cdot 10 - 13 (x + 5)) (x - 5)) i

Simplify

((x (x + 5) - (- 13) \cdot 10) (x - 5) - (x \cdot 10 - 13 (x + 5)) (- 10)) + ((x (x + 5) - (- 13) \cdot 10) (- 10) + (x \cdot 10 - 13 (x + 5)) (x - 5)) i : (x^{3} + 75 x - 1300) + (- 13 x^{2} - 100 x - 975) i

= (x^{3} + 75 x - 1300) + (- 13 x^{2} - 100 x - 975) i

\frac{45 ( e ^{2} - 1 )}{2}

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

\frac{3 ( n + 1 ) ( 2 n + 1 )}{2 n}

\frac{3 ( t + 1 ) ( t - 1 )}{t - 2}

(2 e^{2 r} sin (3 θ)) (s - 2 t)

What is (x-13i)(x+5+10i)(x-5-10i) ?
The solution to (x-13i)(x+5+10i)(x-5-10i) is (x^3+75x-1300)+(-13x^2-100x-975)i