Riješi (x+1)(x-(3-2i))(x-(3+2i))

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

Izračunaj

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

Koraci rješenja

Koristite svojstvo distributivnosti da biste pomnožili x+1 s x-\left(3-2i\right).

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

Koristite svojstvo distributivnosti da biste pomnožili x\left(x-\left(3-2i\right)\right)+x-\left(3-2i\right) s 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 i 3-2i da biste dobili -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 i 3+2i da biste dobili -3-2i.

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

Koristite svojstvo distributivnosti da biste pomnožili x s x+\left(-3+2i\right).

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

Primijenite svojstvo distributivnosti množenjem svakog dijela izraza x^{2}+\left(-3+2i\right)x sa svakim dijelom izraza x+\left(-3-2i\right).

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

Kombinirajte \left(-3-2i\right)x^{2} i \left(-3+2i\right)x^{2} da biste dobili -6x^{2}.

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

Pomnožite -1 i 3-2i da biste dobili -3+2i.

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

Pomnožite -1 i 3+2i da biste dobili -3-2i.

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

Primijenite svojstvo distributivnosti množenjem svakog dijela izraza x+\left(-3+2i\right) sa svakim dijelom izraza x+\left(-3-2i\right).

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

Kombinirajte \left(-3-2i\right)x i \left(-3+2i\right)x da biste dobili -6x.

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

Kombinirajte -6x^{2} i x^{2} da biste dobili -5x^{2}.

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

Kombinirajte 13x i -6x da biste dobili 7x.

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

Proširi

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

Koraci rješenja

Koristite svojstvo distributivnosti da biste pomnožili x+1 s x-\left(3-2i\right).

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

Koristite svojstvo distributivnosti da biste pomnožili x\left(x-\left(3-2i\right)\right)+x-\left(3-2i\right) s 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 i 3-2i da biste dobili -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 i 3+2i da biste dobili -3-2i.

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

Koristite svojstvo distributivnosti da biste pomnožili x s x+\left(-3+2i\right).

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

Primijenite svojstvo distributivnosti množenjem svakog dijela izraza x^{2}+\left(-3+2i\right)x sa svakim dijelom izraza x+\left(-3-2i\right).

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

Kombinirajte \left(-3-2i\right)x^{2} i \left(-3+2i\right)x^{2} da biste dobili -6x^{2}.

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

Pomnožite -1 i 3-2i da biste dobili -3+2i.

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

Pomnožite -1 i 3+2i da biste dobili -3-2i.

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

Primijenite svojstvo distributivnosti množenjem svakog dijela izraza x+\left(-3+2i\right) sa svakim dijelom izraza x+\left(-3-2i\right).

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

Kombinirajte \left(-3-2i\right)x i \left(-3+2i\right)x da biste dobili -6x.

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

Kombinirajte -6x^{2} i x^{2} da biste dobili -5x^{2}.

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

Kombinirajte 13x i -6x da biste dobili 7x.

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