代數計算器

此計算器可逐步解決多種代數問題，並顯示解題步驟。可求斜率、直線方程式、完成平方、進行綜合除法、部分分式分解、分數與多項式的運算、處理等差／等比數列，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:

$$$\left(\color{Crimson}{2 x^{2}}\color{BlueViolet}{- 4 x}+\color{Purple}{2}\right) \cdot \left(\color{DarkBlue}{2 x^{2}}\color{Brown}{- 4 x}+\color{Green}{2}\right)=$$$

$$$=\left(\color{Crimson}{2 x^{2}}\right)\cdot \left(\color{DarkBlue}{2 x^{2}}\right)+\left(\color{Crimson}{2 x^{2}}\right)\cdot \left(\color{Brown}{- 4 x}\right)+\left(\color{Crimson}{2 x^{2}}\right)\cdot \left(\color{Green}{2}\right)+$$$

$$$+\left(\color{BlueViolet}{- 4 x}\right)\cdot \left(\color{DarkBlue}{2 x^{2}}\right)+\left(\color{BlueViolet}{- 4 x}\right)\cdot \left(\color{Brown}{- 4 x}\right)+\left(\color{BlueViolet}{- 4 x}\right)\cdot \left(\color{Green}{2}\right)+$$$

$$$+\left(\color{Purple}{2}\right)\cdot \left(\color{DarkBlue}{2 x^{2}}\right)+\left(\color{Purple}{2}\right)\cdot \left(\color{Brown}{- 4 x}\right)+\left(\color{Purple}{2}\right)\cdot \left(\color{Green}{2}\right)=$$$

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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逐步求解代數問題

Solution