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多項式乘法計算器
逐步進行多項式相乘
此計算器會將兩個多項式（如二次式、二項式、三項式等）相乘，並顯示計算步驟。
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: $$$\left(2 x^{2} - 4 x + 2\right)\cdot \left(2 x^{2} - 4 x + 2\right)=4 x^{4} - 16 x^{3} + 24 x^{2} - 16 x + 4$$$.