Question

x3-3x2y-3xy2-y3

Factorise it

Answer 1

x^3-3x^2y+3xy^2-y^3
(x-y)^3

Answer 2

Given,

x³ - 3x²y + 3xy² - y³

To find,

The factors of x³ - 3x²y + 3xy² - y³.

Solution,

The factor of x³ - 3x²y + 3xy² - y³ will be (x-y)³.

( Note: There is a minor error in the question that has been corrected here. 3xy² should be positive otherwise the question can not be solved.)

We can easily solve this problem by following the given steps.

First, let's arrange the given expression as follows:

x³ - y³ + 3xy² - 3x²y

Taking -3xy common from the last two terms of the expression,

x³ - y³ - 3xy (x - y)

Now, we can see that this is an expression for the identity, (x-y)³.

(x-y)³ = x³ - y³ - 3xy (x - y)

Hence, the factor of x³ - 3x²y + 3xy² - y³ is (x-y)³.