909-Càlculo con Aplicaciones.sagews

Càlculo con Aplicaciones

Libro de Francisco Soler

Elaborado por: Juan Sebastiàn Torres Espìndola

                                [email protected]

Ejercicio 1.5

Efectuar:

3.  35m^2n^3-70m^3

var ('m,n')

(m, n)

factor(35*m^2*n^3-70*m^3)

35*(n^3 - 2*m)*m^2

4.  24a^2xy^2-36x^2y^4

var ('a,x,y')

(a, x, y)

factor (24*a^2*x*y^2-36*x^2*y^4)

-12*(3*x*y^2 - 2*a^2)*x*y^2

5.  x^4y^3z^2+3x^2y^4

var ('x,z,y')

(x, z, y)

factor (x^4*y^3*z^2+3*x^2*y^4)

(x^2*z^2 + 3*y)*x^2*y^3

7.  4x^2-4x-3

var ('x')

x

factor (4*x^2-4*x-3)

(2*x - 3)*(2*x + 1)

8.  a^3-a^2x+ax^2

var ('a,x')

(a, x)

factor (a^3-a^2*x+a*x^2)

(a^2 - a*x + x^2)*a

9.  1-9a^2b^4c^6d^8

var ('a,b,c,d')

(a, b, c, d)

factor (1-9*a^2*b^4*c^6*d^8)

-(3*a*b^2*c^3*d^4 - 1)*(3*a*b^2*c^3*d^4 + 1)

10.  a^6-125b^12

var ('a,b')

(a, b)

factor (a^6-125*b^12)

(a^2 - 5*b^4)*(a^4 + 25*b^8 + 5*a^2*b^4)

12.  1-27a^3b^3

var ('a,b')

(a, b)

factor (1-27*a^3*b^3)

-(3*a*b - 1)*(9*a^2*b^2 + 3*a*b + 1)

13.  4x^(2n)-1/9

var ('x,n')

(x, n)

factor ((4*x^(2*n)-1/9))

1/9*(6*x^n - 1)*(6*x^n + 1)

17.  36n^2-42n+10

var ('n')

n

factor (36*n^2-42*n+10)

2*(3*n - 1)*(6*n - 5)

20.  x^4-32x^2+256

var ('x')

x

factor (x^4-32*x^2+256)

(x - 4)^2*(x + 4)^2

21.  x^4-40x^2+144

var ('x')

x

factor (x^4-40*x^2+144)

(x - 6)*(x - 2)*(x + 2)*(x + 6)