Question

The factors of x³ − 1 + y³ + 3xy are

Options

• (x − 1 + y) (x² + 1 + y² + x + y − xy)

• (x + y + 1) (x² + y² + 1 −xy − x − y)

•  (x − 1 + y) (x² − 1 − y² + x + y + xy)

• 3(x + y −1) (x² + y² − 1)

Answer 1

The given expression to be factorized is  x³ − 1 + y³ + 3xy 

This can be written in the form

 x³ − 1 + y³ + 3xy = `(x)^2 + (-1)^3 + (y)^3 -3 .(x).(-1).(y)`

Recall the formula  `a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2 + b^2 + c^2 - ab - bc - ca)`

Using the above formula, we have 

x³ − 1 + y³ + 3xy 

` = {x+(-1)+ y}{(x)^2 + (-1)^2 + (y)^2 - (x).(-1) - (-1). (y) - (y).(x)}`

` = (x-1 + y)(x^2 + 1 + y^2 + x+ y -xy)`

So, the correct choice is (a).