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多項式の乗算計算機
多項式の掛け算を段階的に行う
この電卓は、2つの多項式（二次式、二項式、三項式など）を、計算手順を表示しながら乗算します。
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: $$$\left(2 x^{2} - 4 x + 2\right)\cdot \left(2 x^{2} - 4 x + 2\right)=4 x^{4} - 16 x^{3} + 24 x^{2} - 16 x + 4$$$.