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Popular Álgebra >

factor 16b^4-81b^4

Solución

factor

16 b^{4} - 81 b^{4}

Solución

- 65 b^{4}

Pasos de solución

16 b^{4} - 81 b^{4}

Reescribir

16 b^{4}

como

(2 b)^{4}

Reescribir

81 b^{4}

como

(3 b)^{4}

= (2 b)^{4} - (3 b)^{4}

Reescribir

(2 b)^{4} - (3 b)^{4}

como

((2 b)^{2})^{2} - ((3 b)^{2})^{2}

= ((2 b)^{2})^{2} - ((3 b)^{2})^{2}

Aplicar la siguiente regla para binomios al cuadrado:

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

((2 b)^{2})^{2} - ((3 b)^{2})^{2} = ((2 b)^{2} + (3 b)^{2}) ((2 b)^{2} - (3 b)^{2})

= ((2 b)^{2} + (3 b)^{2}) ((2 b)^{2} - (3 b)^{2})

Factorizar

(2 b)^{2} - (3 b)^{2} : (2 b + 3 b) (2 b - 3 b)

= ((2 b)^{2} + (3 b)^{2}) (2 b + 3 b) (2 b - 3 b)

Simplificar

((2 b)^{2} + (3 b)^{2}) (2 b + 3 b) (2 b - 3 b) : - 65 b^{4}

= - 65 b^{4}

Ejemplos populares

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f a c t or x sin (1 - x^{2})

factor (1960sqrt(3)-588)/(97)

f a c t or \frac{1960 3 - 588}{97}

factor (c+d)^3-(c-d)^3

f a c t or (c + d)^{3} - (c - d)^{3}

factor 2^{4n+4}-9

f a c t or 2^{4 n + 4} - 9