Question

The factors of x³ −x²y − xy² + y³ are

Options

• (x + y) (x² − xy + y²)

• (x + y) (x² + xy + y²)

• (x + y)² (x − y)

• (x − y)² (x + y)

Answer 1

The given expression to be factorized is

 x³ −x²y − xy² + y³ 

Take common  `x^2` from the first two terms and `-y^2` from the last two terms. That is

 x³ −x²y − xy² + y³ ` = x^2 (x-y) - y^2 (x-y)`

Finally, take common (x-y)from the two terms. That is

x³ −x²y − xy² + y³  = `(x-y)(x^2 - y^2)`

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

                             ` = (x- y)(x+y)(x-y)`

                             ` = (x-y)^2 (x+y)`