代数计算器

该计算器可求解多种代数问题并显示步骤。可求斜率、直线方程，完成平方，进行综合除法、部分分式分解、分式与多项式的运算，处理等差/等比数列等，以及更多功能。

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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:

$$$\left(\color{SaddleBrown}{2 x^{2}}\color{Chartreuse}{- 4 x}+\color{Blue}{2}\right) \cdot \left(\color{GoldenRod}{2 x^{2}}\color{Peru}{- 4 x}+\color{BlueViolet}{2}\right)=$$$

$$$=\left(\color{SaddleBrown}{2 x^{2}}\right)\cdot \left(\color{GoldenRod}{2 x^{2}}\right)+\left(\color{SaddleBrown}{2 x^{2}}\right)\cdot \left(\color{Peru}{- 4 x}\right)+\left(\color{SaddleBrown}{2 x^{2}}\right)\cdot \left(\color{BlueViolet}{2}\right)+$$$

$$$+\left(\color{Chartreuse}{- 4 x}\right)\cdot \left(\color{GoldenRod}{2 x^{2}}\right)+\left(\color{Chartreuse}{- 4 x}\right)\cdot \left(\color{Peru}{- 4 x}\right)+\left(\color{Chartreuse}{- 4 x}\right)\cdot \left(\color{BlueViolet}{2}\right)+$$$

$$$+\left(\color{Blue}{2}\right)\cdot \left(\color{GoldenRod}{2 x^{2}}\right)+\left(\color{Blue}{2}\right)\cdot \left(\color{Peru}{- 4 x}\right)+\left(\color{Blue}{2}\right)\cdot \left(\color{BlueViolet}{2}\right)=$$$

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: $$$\left(2 x^{2} - 4 x + 2\right)\cdot \left(2 x^{2} - 4 x + 2\right)=4 x^{4} - 16 x^{3} + 24 x^{2} - 16 x + 4$$$.

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逐步求解代数问题

Solution