Question

factorise (x+y)^3-(x^3+y^3)

Answer 1

Answer:

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.

Answer 2

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

= (x+y)³-(x+y)(x²-xy+y²)

= (x+y)[(x+y)²-(x²-xy+y²))]

= (x+y)(x²+2xy+y²-x²+xy-y²)

= (x+y)(3xy)

= 3xy(x+y) Ans.