Question

What is the factor of ( x + y)^3 - ( x^3 + y^3 )

Answer 1

Answer:

Step-by-step explanation:

(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.

Answer 2

Step-by-step explanation:

(x + y)³ - (x³ + y³)

= x³ + y³ + 3xy (x+y) -x³ -y³

= 3xy (x+y)

Hence, 3xy and (x+y) are the factors of the equation