Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición de multiplicadores/ a^8+b^8

Factorizar el polinomio a^8+b^8

Expresión a simplificar:

Solución

Ha introducido [src] 
 8    8
a  + b
a8+b8a^{8} + b^{8} 
a^8 + b^8
Factorización [src] 
                                                                                                                                                                                                    /      /           ___________              ___________                ___________                ___________\\ /      /           ___________              ___________                ___________                ___________\\ /      /             ___________              ___________                ___________                ___________\\ /      /           ___________              ___________                ___________                ___________\\
                                                                                                                                                                                                    |      |          /       ___              /       ___                /       ___                /       ___ || |      |          /       ___              /       ___                /       ___                /       ___ || |      |            /       ___              /       ___                /       ___                /       ___ || |      |          /       ___              /       ___                /       ___                /       ___ ||
/      /       ___________          ___________\\ /      /     ___________          ___________\\ /      /       ___________          ___________\\ /      /     ___________          ___________\\ |      |  ___    /  1   \/ 2       ___    /  1   \/ 2         ___    /  1   \/ 2         ___    /  1   \/ 2  || |      |  ___    /  1   \/ 2       ___    /  1   \/ 2         ___    /  1   \/ 2         ___    /  1   \/ 2  || |      |    ___    /  1   \/ 2       ___    /  1   \/ 2         ___    /  1   \/ 2         ___    /  1   \/ 2  || |      |  ___    /  1   \/ 2       ___    /  1   \/ 2         ___    /  1   \/ 2         ___    /  1   \/ 2  ||
|      |      /       ___          /       ___ || |      |    /       ___          /       ___ || |      |      /       ___          /       ___ || |      |    /       ___          /       ___ || |      |\/ 2 *  /   - + -----    \/ 2 *  /   - - -----    I*\/ 2 *  /   - - -----    I*\/ 2 *  /   - + ----- || |      |\/ 2 *  /   - - -----    \/ 2 *  /   - + -----    I*\/ 2 *  /   - - -----    I*\/ 2 *  /   - + ----- || |      |  \/ 2 *  /   - - -----    \/ 2 *  /   - + -----    I*\/ 2 *  /   - + -----    I*\/ 2 *  /   - - ----- || |      |\/ 2 *  /   - - -----    \/ 2 *  /   - + -----    I*\/ 2 *  /   - - -----    I*\/ 2 *  /   - + ----- ||
|      |     /  1   \/ 2          /  1   \/ 2  || |      |   /  1   \/ 2          /  1   \/ 2  || |      |     /  1   \/ 2          /  1   \/ 2  || |      |   /  1   \/ 2          /  1   \/ 2  || |      |      \/    2     4            \/    2     4              \/    2     4              \/    2     4   || |      |      \/    2     4            \/    2     4              \/    2     4              \/    2     4   || |      |        \/    2     4            \/    2     4              \/    2     4              \/    2     4   || |      |      \/    2     4            \/    2     4              \/    2     4              \/    2     4   ||
|a - b*|-   /   - - -----  + I*  /   - + ----- ||*|a - b*|  /   - - -----  - I*  /   - + ----- ||*|a - b*|-   /   - + -----  - I*  /   - - ----- ||*|a - b*|  /   - + -----  + I*  /   - - ----- ||*|a - b*|---------------------- - ---------------------- + ------------------------ + ------------------------||*|a - b*|---------------------- + ---------------------- + ------------------------ - ------------------------||*|a - b*|- ---------------------- - ---------------------- + ------------------------ - ------------------------||*|a - b*|---------------------- - ---------------------- - ------------------------ - ------------------------||
\      \  \/    2     4        \/    2     4   // \      \\/    2     4        \/    2     4   // \      \  \/    2     4        \/    2     4   // \      \\/    2     4        \/    2     4   // \      \          2                        2                         2                          2            // \      \          2                        2                         2                          2            // \      \            2                        2                         2                          2            // \      \          2                        2                         2                          2            //
(a−b(−12−24+i24+12))(a−b(12−24−i24+12))(a−b(−24+12−i12−24))(a−b(24+12+i12−24))(a−b(−212−242+224+122+2i12−242+2i24+122))(a−b(212−242+224+122−2i24+122+2i12−242))(a−b(−224+122−212−242−2i12−242+2i24+122))(a−b(−224+122+212−242−2i24+122−2i12−242))\left(a - b \left(- \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} + i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right)\right) \left(a - b \left(\sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}} - i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}\right)\right) \left(a - b \left(- \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} - i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}\right)\right) \left(a - b \left(\sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}} + i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}\right)\right) \left(a - b \left(- \frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2}\right)\right) \left(a - b \left(\frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2}\right)\right) \left(a - b \left(- \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} - \frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} + \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2}\right)\right) \left(a - b \left(- \frac{\sqrt{2} \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} + \frac{\sqrt{2} \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{\sqrt{2}}{4} + \frac{1}{2}}}{2} - \frac{\sqrt{2} i \sqrt{\frac{1}{2} - \frac{\sqrt{2}}{4}}}{2}\right)\right) 
(((((((a - b*(-sqrt(1/2 - sqrt(2)/4) + i*sqrt(1/2 + sqrt(2)/4)))*(a - b*(sqrt(1/2 - sqrt(2)/4) - i*sqrt(1/2 + sqrt(2)/4))))*(a - b*(-sqrt(1/2 + sqrt(2)/4) - i*sqrt(1/2 - sqrt(2)/4))))*(a - b*(sqrt(1/2 + sqrt(2)/4) + i*sqrt(1/2 - sqrt(2)/4))))*(a - b*(sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 - sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2)))*(a - b*(sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 + sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2)))*(a - b*(-sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 + i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2)))*(a - b*(sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 - sqrt(2)/4)/2 - i*sqrt(2)*sqrt(1/2 + sqrt(2)/4)/2))
Respuesta numérica [src] 
a^8 + b^8
a^8 + b^8
    © Sr Examen – Калькулятор