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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.
Solution
Your input: multiply $$$2 x^{2} - 4 x + 2$$$ by $$$2 x^{2} - 4 x + 2$$$.
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:
$$$\left(\color{Chartreuse}{2 x^{2}}\color{Green}{- 4 x}+\color{Crimson}{2}\right) \cdot \left(\color{Fuchsia}{2 x^{2}}\color{Purple}{- 4 x}+\color{DarkBlue}{2}\right)=$$$
$$$=\left(\color{Chartreuse}{2 x^{2}}\right)\cdot \left(\color{Fuchsia}{2 x^{2}}\right)+\left(\color{Chartreuse}{2 x^{2}}\right)\cdot \left(\color{Purple}{- 4 x}\right)+\left(\color{Chartreuse}{2 x^{2}}\right)\cdot \left(\color{DarkBlue}{2}\right)+$$$
$$$+\left(\color{Green}{- 4 x}\right)\cdot \left(\color{Fuchsia}{2 x^{2}}\right)+\left(\color{Green}{- 4 x}\right)\cdot \left(\color{Purple}{- 4 x}\right)+\left(\color{Green}{- 4 x}\right)\cdot \left(\color{DarkBlue}{2}\right)+$$$
$$$+\left(\color{Crimson}{2}\right)\cdot \left(\color{Fuchsia}{2 x^{2}}\right)+\left(\color{Crimson}{2}\right)\cdot \left(\color{Purple}{- 4 x}\right)+\left(\color{Crimson}{2}\right)\cdot \left(\color{DarkBlue}{2}\right)=$$$
Simplify the products:
$$$=4 x^{4}- 8 x^{3}+4 x^{2}+$$$
$$$- 8 x^{3}+16 x^{2}- 8 x+$$$
$$$+4 x^{2}- 8 x+4=$$$
Simplify further:
$$$=4 x^{4} - 16 x^{3} + 24 x^{2} - 16 x + 4$$$
Answer: $$$\left(2 x^{2} - 4 x + 2\right)\cdot \left(2 x^{2} - 4 x + 2\right)=4 x^{4} - 16 x^{3} + 24 x^{2} - 16 x + 4$$$.