Question

Which of the following is a factor of (x + y)3 – (x3 + y3 )?

(A) x2 + y2 + 2xy

(B) x2 + y2 – xy

(C) xy2

(D) 3xy

Answer 1

(d) 3xy

Now, (x+ y)3 – (x3 + y3)

= (x + y) – (x + y)(x2– xy + y2)
[using identity, a3 + b3 = (a + b)(a2 -ab+ b2)] = (x+ y)[(x+ y)2 -(x2 -xy+ y2)]

= (x+ y)(x2+ y2+ 2xy- x2+ xy- y2)
[using identity, (a + b)2 = a2 + b2 + 2 ab)]

= (x + y) (3xy)

Hence, one of the factor of given polynomial is 3xy.