1115.sagews

1) Factorizar la expresion dada: 

a) $35*m^2*n^3 - 70*m^3$

var('m,n')

(m, n)

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

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

b) $24*a^2*x*y^2 - 36*x^2*y^4$

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

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

var('x,y,a')

(x, y, a)

c) $(x+1) * (x-2) + 3*y* (x - 2)$

var('x,y')

(x, y)

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

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

d) $a^3 - a^2* x + a*x^2$

var('a,x')

(a, x)

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

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

e) $1 - 27*a^3*b^3$

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)

f) $(36n^2 - 42*n + 10)$

var('n')

n

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

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