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多项式乘法计算器
逐步计算多项式的乘积
该计算器将对两个多项式（如二次多项式、二项式、三项式等）进行相乘，并显示步骤。
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: $$$\left(2 x^{2} - 4 x + 2\right)\cdot \left(2 x^{2} - 4 x + 2\right)=4 x^{4} - 16 x^{3} + 24 x^{2} - 16 x + 4$$$.