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Calculadora de álgebra

Resolver problemas de álgebra paso a paso

Esta calculadora resuelve muchos problemas de álgebra con los pasos que se muestran. Encuentra pendientes, ecuaciones lineales, completa el cuadrado, realiza divisiones sintéticas, descomposición de fracciones parciales, operaciones con fracciones y polinomios, maneja secuencias aritméticas/geométricas y mucho más.
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Enlace permanente: Calculadora de multiplicación de polinomios

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:

$$$\left(\color{DeepPink}{2 x^{2}}\color{Red}{- 4 x}+\color{Chartreuse}{2}\right) \cdot \left(\color{Chocolate}{2 x^{2}}\color{Blue}{- 4 x}+\color{SaddleBrown}{2}\right)=$$$

$$$=\left(\color{DeepPink}{2 x^{2}}\right)\cdot \left(\color{Chocolate}{2 x^{2}}\right)+\left(\color{DeepPink}{2 x^{2}}\right)\cdot \left(\color{Blue}{- 4 x}\right)+\left(\color{DeepPink}{2 x^{2}}\right)\cdot \left(\color{SaddleBrown}{2}\right)+$$$

$$$+\left(\color{Red}{- 4 x}\right)\cdot \left(\color{Chocolate}{2 x^{2}}\right)+\left(\color{Red}{- 4 x}\right)\cdot \left(\color{Blue}{- 4 x}\right)+\left(\color{Red}{- 4 x}\right)\cdot \left(\color{SaddleBrown}{2}\right)+$$$

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

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