No AI is used
  1. Startseite
  2. Rechner
  3. Rechner: Algebra I
  4. Algebra-Rechner

Rechner zur Multiplikation von Polynomen

Polynome Schritt für Schritt multiplizieren

Der Rechner multipliziert zwei Polynome (z. B. quadratische Polynome, Binome, Trinome usw.) und zeigt die Rechenschritte.

First polynomial:

Second polynomial:

Wenn der Rechner nicht wie erwartet funktioniert hat oder Sie einen Fehler melden oder Feedback geben möchten, kontaktieren Sie uns bitte.

Solution

Your input: multiply $$$3 x^{8} - 5 x^{3} - x^{2} + 2 x + 1$$$ by $$$2 x^{2} - 5 x + 3$$$.

To multiply polynomials, multiply each term of the first polynomial by every term of the second polynomial. Then simplify the products and add them. Finally, simplify further if possible.

So, perform the first step:

$$$\left(\color{DeepPink}{3 x^{8}}\color{Magenta}{- 5 x^{3}}\color{Peru}{- x^{2}}+\color{Chocolate}{2 x}+\color{Brown}{1}\right) \cdot \left(\color{Chartreuse}{2 x^{2}}\color{Green}{- 5 x}+\color{Red}{3}\right)=$$$

$$$=\left(\color{DeepPink}{3 x^{8}}\right)\cdot \left(\color{Chartreuse}{2 x^{2}}\right)+\left(\color{DeepPink}{3 x^{8}}\right)\cdot \left(\color{Green}{- 5 x}\right)+\left(\color{DeepPink}{3 x^{8}}\right)\cdot \left(\color{Red}{3}\right)+$$$

$$$+\left(\color{Magenta}{- 5 x^{3}}\right)\cdot \left(\color{Chartreuse}{2 x^{2}}\right)+\left(\color{Magenta}{- 5 x^{3}}\right)\cdot \left(\color{Green}{- 5 x}\right)+\left(\color{Magenta}{- 5 x^{3}}\right)\cdot \left(\color{Red}{3}\right)+$$$

$$$+\left(\color{Peru}{- x^{2}}\right)\cdot \left(\color{Chartreuse}{2 x^{2}}\right)+\left(\color{Peru}{- x^{2}}\right)\cdot \left(\color{Green}{- 5 x}\right)+\left(\color{Peru}{- x^{2}}\right)\cdot \left(\color{Red}{3}\right)+$$$

$$$+\left(\color{Chocolate}{2 x}\right)\cdot \left(\color{Chartreuse}{2 x^{2}}\right)+\left(\color{Chocolate}{2 x}\right)\cdot \left(\color{Green}{- 5 x}\right)+\left(\color{Chocolate}{2 x}\right)\cdot \left(\color{Red}{3}\right)+$$$

$$$+\left(\color{Brown}{1}\right)\cdot \left(\color{Chartreuse}{2 x^{2}}\right)+\left(\color{Brown}{1}\right)\cdot \left(\color{Green}{- 5 x}\right)+\left(\color{Brown}{1}\right)\cdot \left(\color{Red}{3}\right)=$$$

Simplify the products:

$$$=6 x^{10}- 15 x^{9}+9 x^{8}+$$$

$$$- 10 x^{5}+25 x^{4}- 15 x^{3}+$$$

$$$- 2 x^{4}+5 x^{3}- 3 x^{2}+$$$

$$$+4 x^{3}- 10 x^{2}+6 x+$$$

$$$+2 x^{2}- 5 x+3=$$$

Simplify further:

$$$=6 x^{10} - 15 x^{9} + 9 x^{8} - 10 x^{5} + 23 x^{4} - 6 x^{3} - 11 x^{2} + x + 3$$$

Answer: $$$\left(3 x^{8} - 5 x^{3} - x^{2} + 2 x + 1\right)\cdot \left(2 x^{2} - 5 x + 3\right)=6 x^{10} - 15 x^{9} + 9 x^{8} - 10 x^{5} + 23 x^{4} - 6 x^{3} - 11 x^{2} + x + 3$$$.