Rešite (x+1)(x-(3-2i))(x-(3+2i))

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

Ovrednoti

$$\left(x+1\right)\left(x+\left(-3-2i\right)\right)\left(x+\left(-3+2i\right)\right)$$

Koraki rešitve

Uporabite distributivnost, da pomnožite x+1 s/z x-\left(3-2i\right).

$$\left(x\left(x-\left(3-2i\right)\right)+x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Uporabite distributivnost, da pomnožite x\left(x-\left(3-2i\right)\right)+x-\left(3-2i\right) s/z x-\left(3+2i\right).

$$x\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Pomnožite -1 in 3-2i, da dobite -3+2i.

$$x\left(x+\left(-3+2i\right)\right)\left(x-\left(3+2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Pomnožite -1 in 3+2i, da dobite -3-2i.

$$x\left(x+\left(-3+2i\right)\right)\left(x+\left(-3-2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Uporabite distributivnost, da pomnožite x s/z x+\left(-3+2i\right).

$$\left(x^{2}+\left(-3+2i\right)x\right)\left(x+\left(-3-2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Uporabite distributivnost tako, da pomnožite vsako vrednost x^{2}+\left(-3+2i\right)x z vsako vrednostjo x+\left(-3-2i\right).

$$x^{3}+\left(-3-2i\right)x^{2}+\left(-3+2i\right)x^{2}+13x+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Združite \left(-3-2i\right)x^{2} in \left(-3+2i\right)x^{2}, da dobite -6x^{2}.

$$x^{3}-6x^{2}+13x+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Pomnožite -1 in 3-2i, da dobite -3+2i.

$$x^{3}-6x^{2}+13x+\left(x+\left(-3+2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Pomnožite -1 in 3+2i, da dobite -3-2i.

$$x^{3}-6x^{2}+13x+\left(x+\left(-3+2i\right)\right)\left(x+\left(-3-2i\right)\right)$$

Uporabite distributivnost tako, da pomnožite vsako vrednost x+\left(-3+2i\right) z vsako vrednostjo x+\left(-3-2i\right).

$$x^{3}-6x^{2}+13x+x^{2}+\left(-3-2i\right)x+\left(-3+2i\right)x+13$$

Združite \left(-3-2i\right)x in \left(-3+2i\right)x, da dobite -6x.

$$x^{3}-6x^{2}+13x+x^{2}-6x+13$$

Združite -6x^{2} in x^{2}, da dobite -5x^{2}.

$$x^{3}-5x^{2}+13x-6x+13$$

Združite 13x in -6x, da dobite 7x.

$$x^{3}-5x^{2}+7x+13$$

Razširi

$$x^{3}-5x^{2}+7x+13$$

Koraki rešitve

Uporabite distributivnost, da pomnožite x+1 s/z x-\left(3-2i\right).

$$\left(x\left(x-\left(3-2i\right)\right)+x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Uporabite distributivnost, da pomnožite x\left(x-\left(3-2i\right)\right)+x-\left(3-2i\right) s/z x-\left(3+2i\right).

$$x\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Pomnožite -1 in 3-2i, da dobite -3+2i.

$$x\left(x+\left(-3+2i\right)\right)\left(x-\left(3+2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Pomnožite -1 in 3+2i, da dobite -3-2i.

$$x\left(x+\left(-3+2i\right)\right)\left(x+\left(-3-2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Uporabite distributivnost, da pomnožite x s/z x+\left(-3+2i\right).

$$\left(x^{2}+\left(-3+2i\right)x\right)\left(x+\left(-3-2i\right)\right)+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Uporabite distributivnost tako, da pomnožite vsako vrednost x^{2}+\left(-3+2i\right)x z vsako vrednostjo x+\left(-3-2i\right).

$$x^{3}+\left(-3-2i\right)x^{2}+\left(-3+2i\right)x^{2}+13x+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Združite \left(-3-2i\right)x^{2} in \left(-3+2i\right)x^{2}, da dobite -6x^{2}.

$$x^{3}-6x^{2}+13x+\left(x-\left(3-2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Pomnožite -1 in 3-2i, da dobite -3+2i.

$$x^{3}-6x^{2}+13x+\left(x+\left(-3+2i\right)\right)\left(x-\left(3+2i\right)\right)$$

Pomnožite -1 in 3+2i, da dobite -3-2i.

$$x^{3}-6x^{2}+13x+\left(x+\left(-3+2i\right)\right)\left(x+\left(-3-2i\right)\right)$$

Uporabite distributivnost tako, da pomnožite vsako vrednost x+\left(-3+2i\right) z vsako vrednostjo x+\left(-3-2i\right).

$$x^{3}-6x^{2}+13x+x^{2}+\left(-3-2i\right)x+\left(-3+2i\right)x+13$$

Združite \left(-3-2i\right)x in \left(-3+2i\right)x, da dobite -6x.

$$x^{3}-6x^{2}+13x+x^{2}-6x+13$$

Združite -6x^{2} in x^{2}, da dobite -5x^{2}.

$$x^{3}-5x^{2}+13x-6x+13$$

Združite 13x in -6x, da dobite 7x.

$$x^{3}-5x^{2}+7x+13$$