Question

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

Answer 1

Step-by-step explanation:

The Sum of Cubes

A binomial in the form a3 + b3 can be factored as (a + b)(a2 – ab + b2). Examples: The factored form of x3 + 64 is (x + 4)(x2 – 4x + 16). The factored form of 8x3 + y3 is (2x + y)(4x2 – 2xy + y2).

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Answer 2

Answer:

3xy

Step-by-step explanation:

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.