factor x^8-4x^4y^4+3y^8

Solución

factor

x^{8} - 4 x^{4} y^{4} + 3 y^{8}

(x^{2} + y^{2}) (x + y) (x - y) (x^{4} - 3 y^{4})

Pasos de solución

x^{8} - 4 x^{4} y^{4} + 3 y^{8}

Factorizar la expresión

= (x^{8} - x^{4} y^{4}) + (- 3 x^{4} y^{4} + 3 y^{8})

Factorizar

x^{4}

x^{8} - x^{4} y^{4}

x^{4} (x^{4} - y^{4})

Factorizar

- 3 y^{4}

- 3 x^{4} y^{4} + 3 y^{8}

- 3 y^{4} (x^{4} - y^{4})

= x^{4} (x^{4} - y^{4}) - 3 y^{4} (x^{4} - y^{4})

Factorizar el termino común

x^{4} - y^{4}

= (x^{4} - y^{4}) (x^{4} - 3 y^{4})

Factorizar

x^{4} - y^{4} : (x^{2} + y^{2}) (x + y) (x - y)

= (x^{2} + y^{2}) (x + y) (x - y) (x^{4} - 3 y^{4})

f a c t or (n + 3)^{2} + 2 n

f a c t or k^{r + m} - 4 k^{r} + k^{m} - 4

d ec t o f r a c 7.6

f a c t or 2 x (3 x^{3} - x^{3})

f a c t or m^{2} + 2 m + (- 1)