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calculadora de álgebra

Resolva problemas de álgebra passo a passo

Esta calculadora resolve muitos problemas de álgebra com as etapas mostradas. Encontra inclinações, equações de linha, completa o quadrado, executa divisão sintética, decomposição de fração parcial, operações em frações e polinômios, lida com sequências aritméticas/geométricas e muito mais.
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First polynomial:

Second polynomial:

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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:

$$$\left(\color{Blue}{2 x^{2}}\color{Brown}{- 4 x}+\color{BlueViolet}{2}\right) \cdot \left(\color{DarkCyan}{2 x^{2}}\color{DarkBlue}{- 4 x}+\color{Magenta}{2}\right)=$$$

$$$=\left(\color{Blue}{2 x^{2}}\right)\cdot \left(\color{DarkCyan}{2 x^{2}}\right)+\left(\color{Blue}{2 x^{2}}\right)\cdot \left(\color{DarkBlue}{- 4 x}\right)+\left(\color{Blue}{2 x^{2}}\right)\cdot \left(\color{Magenta}{2}\right)+$$$

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

$$$+\left(\color{BlueViolet}{2}\right)\cdot \left(\color{DarkCyan}{2 x^{2}}\right)+\left(\color{BlueViolet}{2}\right)\cdot \left(\color{DarkBlue}{- 4 x}\right)+\left(\color{BlueViolet}{2}\right)\cdot \left(\color{Magenta}{2}\right)=$$$

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