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Simplificación de expresiones/ Descomposición de multiplicadores/ 81*m^6-72*m^3*n^2/25+64*n^4/25

Factorizar el polinomio 81*m^6-72*m^3*n^2/25+64*n^4/25

Expresión a simplificar:

Solución

Ha introducido [src] 
            3  2       4
    6   72*m *n    64*n 
81*m  - -------- + -----
           25        25
64n425+(81m6−72m3n225)\frac{64 n^{4}}{25} + \left(81 m^{6} - \frac{72 m^{3} n^{2}}{25}\right) 
81*m^6 - (72*m^3)*n^2/25 + (64*n^4)/25
Simplificación general [src] 
            4       3  2
    6   64*n    72*m *n 
81*m  + ----- - --------
          25       25
81m6−72m3n225+64n42581 m^{6} - \frac{72 m^{3} n^{2}}{25} + \frac{64 n^{4}}{25} 
81*m^6 + 64*n^4/25 - 72*m^3*n^2/25
Factorización [src] 
                                                                    /         ______________________                ______________________\ /         ______________________                ______________________\ /         ______________________                ______________________\ /         ______________________                ______________________\
                                                                    |        /    2         ____  2                /    2         ____  2 | |        /    2         ____  2                /    2         ____  2 | |        /    2         ____  2                /    2         ____  2 | |        /    2         ____  2                /    2         ____  2 |
/         ______________________\ /         ______________________\ |       /  4*n    4*I*\/ 11 *n         ___    /  4*n    4*I*\/ 11 *n  | |       /  4*n    4*I*\/ 11 *n         ___    /  4*n    4*I*\/ 11 *n  | |       /  4*n    4*I*\/ 11 *n         ___    /  4*n    4*I*\/ 11 *n  | |       /  4*n    4*I*\/ 11 *n         ___    /  4*n    4*I*\/ 11 *n  |
|        /    2         ____  2 | |        /    2         ____  2 | |    3 /   ---- - -------------    I*\/ 3 *3 /   ---- - ------------- | |    3 /   ---- - -------------    I*\/ 3 *3 /   ---- - ------------- | |    3 /   ---- + -------------    I*\/ 3 *3 /   ---- + ------------- | |    3 /   ---- + -------------    I*\/ 3 *3 /   ---- + ------------- |
|       /  4*n    4*I*\/ 11 *n  | |       /  4*n    4*I*\/ 11 *n  | |    \/    225          75                 \/    225          75      | |    \/    225          75                 \/    225          75      | |    \/    225          75                 \/    225          75      | |    \/    225          75                 \/    225          75      |
|m - 3 /   ---- - ------------- |*|m - 3 /   ---- + ------------- |*|m + --------------------------- + -----------------------------------|*|m + --------------------------- - -----------------------------------|*|m + --------------------------- + -----------------------------------|*|m + --------------------------- - -----------------------------------|
\    \/    225          75      / \    \/    225          75      / \                 2                                 2                 / \                 2                                 2                 / \                 2                                 2                 / \                 2                                 2                 /
(m−4n2225−411in2753)(m−4n2225+411in2753)(m+(4n2225−411in27532+3i4n2225−411in27532))(m+(4n2225−411in27532−3i4n2225−411in27532))(m+(4n2225+411in27532+3i4n2225+411in27532))(m+(4n2225+411in27532−3i4n2225+411in27532))\left(m - \sqrt[3]{\frac{4 n^{2}}{225} - \frac{4 \sqrt{11} i n^{2}}{75}}\right) \left(m - \sqrt[3]{\frac{4 n^{2}}{225} + \frac{4 \sqrt{11} i n^{2}}{75}}\right) \left(m + \left(\frac{\sqrt[3]{\frac{4 n^{2}}{225} - \frac{4 \sqrt{11} i n^{2}}{75}}}{2} + \frac{\sqrt{3} i \sqrt[3]{\frac{4 n^{2}}{225} - \frac{4 \sqrt{11} i n^{2}}{75}}}{2}\right)\right) \left(m + \left(\frac{\sqrt[3]{\frac{4 n^{2}}{225} - \frac{4 \sqrt{11} i n^{2}}{75}}}{2} - \frac{\sqrt{3} i \sqrt[3]{\frac{4 n^{2}}{225} - \frac{4 \sqrt{11} i n^{2}}{75}}}{2}\right)\right) \left(m + \left(\frac{\sqrt[3]{\frac{4 n^{2}}{225} + \frac{4 \sqrt{11} i n^{2}}{75}}}{2} + \frac{\sqrt{3} i \sqrt[3]{\frac{4 n^{2}}{225} + \frac{4 \sqrt{11} i n^{2}}{75}}}{2}\right)\right) \left(m + \left(\frac{\sqrt[3]{\frac{4 n^{2}}{225} + \frac{4 \sqrt{11} i n^{2}}{75}}}{2} - \frac{\sqrt{3} i \sqrt[3]{\frac{4 n^{2}}{225} + \frac{4 \sqrt{11} i n^{2}}{75}}}{2}\right)\right) 
(((((m - (4*n^2/225 - 4*i*sqrt(11)*n^2/75)^(1/3))*(m - (4*n^2/225 + 4*i*sqrt(11)*n^2/75)^(1/3)))*(m + (4*n^2/225 - 4*i*sqrt(11)*n^2/75)^(1/3)/2 + i*sqrt(3)*(4*n^2/225 - 4*i*sqrt(11)*n^2/75)^(1/3)/2))*(m + (4*n^2/225 - 4*i*sqrt(11)*n^2/75)^(1/3)/2 - i*sqrt(3)*(4*n^2/225 - 4*i*sqrt(11)*n^2/75)^(1/3)/2))*(m + (4*n^2/225 + 4*i*sqrt(11)*n^2/75)^(1/3)/2 + i*sqrt(3)*(4*n^2/225 + 4*i*sqrt(11)*n^2/75)^(1/3)/2))*(m + (4*n^2/225 + 4*i*sqrt(11)*n^2/75)^(1/3)/2 - i*sqrt(3)*(4*n^2/225 + 4*i*sqrt(11)*n^2/75)^(1/3)/2)
Respuesta numérica [src] 
81.0*m^6 + 2.56*n^4 - 2.88*m^3*n^2
81.0*m^6 + 2.56*n^4 - 2.88*m^3*n^2
Combinatoria [src] 
            4       3  2
    6   64*n    72*m *n 
81*m  + ----- - --------
          25       25
81m6−72m3n225+64n42581 m^{6} - \frac{72 m^{3} n^{2}}{25} + \frac{64 n^{4}}{25} 
81*m^6 + 64*n^4/25 - 72*m^3*n^2/25
Parte trigonométrica [src] 
            4       3  2
    6   64*n    72*m *n 
81*m  + ----- - --------
          25       25
81m6−72m3n225+64n42581 m^{6} - \frac{72 m^{3} n^{2}}{25} + \frac{64 n^{4}}{25} 
81*m^6 + 64*n^4/25 - 72*m^3*n^2/25
Unión de expresiones racionales [src] 
    4      3 /     2        3\
64*n  + 9*m *\- 8*n  + 225*m /
------------------------------
              25
9m3(225m3−8n2)+64n425\frac{9 m^{3} \left(225 m^{3} - 8 n^{2}\right) + 64 n^{4}}{25} 
(64*n^4 + 9*m^3*(-8*n^2 + 225*m^3))/25
Denominador racional [src] 
    4         6       3  2
64*n  + 2025*m  - 72*m *n 
--------------------------
            25
2025m6−72m3n2+64n425\frac{2025 m^{6} - 72 m^{3} n^{2} + 64 n^{4}}{25} 
(64*n^4 + 2025*m^6 - 72*m^3*n^2)/25
Potencias [src] 
            4       3  2
    6   64*n    72*m *n 
81*m  + ----- - --------
          25       25
81m6−72m3n225+64n42581 m^{6} - \frac{72 m^{3} n^{2}}{25} + \frac{64 n^{4}}{25} 
81*m^6 + 64*n^4/25 - 72*m^3*n^2/25
Denominador común [src] 
            4       3  2
    6   64*n    72*m *n 
81*m  + ----- - --------
          25       25
81m6−72m3n225+64n42581 m^{6} - \frac{72 m^{3} n^{2}}{25} + \frac{64 n^{4}}{25} 
81*m^6 + 64*n^4/25 - 72*m^3*n^2/25
Compilar la expresión [src] 
            4       3  2
    6   64*n    72*m *n 
81*m  + ----- - --------
          25       25
81m6−72m3n225+64n42581 m^{6} - \frac{72 m^{3} n^{2}}{25} + \frac{64 n^{4}}{25} 
81*m^6 + 64*n^4/25 - 72*m^3*n^2/25
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