Question

using factor theorem show that( X + Y )(Y + Z) and(
Z+ X) are the factors of X + Y + Z whole cube minus x cube minus y cube minus Z cube​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

Sol: Let f(x) = (x+y+z)3 - x3 - y3 - z3 To show (x + y) is a factor of f(x), we find the zero of the binomial (x + y). (x + y) = 0 ⇒ x = -y f(-y) = (-y +y +z)3 - (-y)3 - y3 - z3 = z3 + y3 - y3 - z3 = 0 Therefore, (x + y) is a factor of (x+y+z)3 - x3 - y3 - z3. The given expression is a cyclic expression in x, y and z, so the factors of the expression are also cyclic. Therefore (x + y), (y + z) are the other factors of the polynomial. Hence, (x + y), (y + z) and (z + x) are the factors of (x+y+z)3 - x3 - y3 - z3.