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Υπολογιστής Πολλαπλασιασμού Πολυωνύμων
Πολλαπλασιάστε πολυώνυμα βήμα προς βήμα
Η αριθμομηχανή θα πολλαπλασιάσει δύο πολυώνυμα (δευτέρου βαθμού, διώνυμα, τριώνυμα κ.λπ.), με αναλυτικά βήματα.
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:
$$$\left(\color{BlueViolet}{2 x^{2}}\color{Red}{- 4 x}+\color{Purple}{2}\right) \cdot \left(\color{Crimson}{2 x^{2}}\color{Fuchsia}{- 4 x}+\color{Violet}{2}\right)=$$$
$$$=\left(\color{BlueViolet}{2 x^{2}}\right)\cdot \left(\color{Crimson}{2 x^{2}}\right)+\left(\color{BlueViolet}{2 x^{2}}\right)\cdot \left(\color{Fuchsia}{- 4 x}\right)+\left(\color{BlueViolet}{2 x^{2}}\right)\cdot \left(\color{Violet}{2}\right)+$$$
$$$+\left(\color{Red}{- 4 x}\right)\cdot \left(\color{Crimson}{2 x^{2}}\right)+\left(\color{Red}{- 4 x}\right)\cdot \left(\color{Fuchsia}{- 4 x}\right)+\left(\color{Red}{- 4 x}\right)\cdot \left(\color{Violet}{2}\right)+$$$
$$$+\left(\color{Purple}{2}\right)\cdot \left(\color{Crimson}{2 x^{2}}\right)+\left(\color{Purple}{2}\right)\cdot \left(\color{Fuchsia}{- 4 x}\right)+\left(\color{Purple}{2}\right)\cdot \left(\color{Violet}{2}\right)=$$$
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: $$$\left(2 x^{2} - 4 x + 2\right)\cdot \left(2 x^{2} - 4 x + 2\right)=4 x^{4} - 16 x^{3} + 24 x^{2} - 16 x + 4$$$.