Question

14. The product of two numbers is (x6 – y6). If one of the numbers is (x - y), then find the other​

Answer 1

Answer:

We know the identity a3−b3=(a−b)(a2+b2+ab)

Using the above identity, the equation x6−y6 can be factorised as follows:

x6−y6=(x2)3−(y2)3=(x2−y2)[(x2)2+(y2)2+(x2×y2)]=(x−y)(x+y)(x2+y2+xy)(x2+y2−xy) 

(using identities a2−b2=(a+b)(a−b) and a4+b4+a2b2=(a2+b2+ab)(a2+b2−ab) ) 

Hence,