Question

12. Find the LCM x3+y3, x3-y3, x4+x2y2+y4​

Answer 1

Given, x

3

+y

3

,x

3

−y

3

,x

4

+x

2

y

2

+y

4

⇒x

3

+y

3

=(x+y)(x

2

−xy+x

2

)

⇒x

3

−y

3

=(x−y)(x

2

+xy+y

2

)

⇒x

4

+x

2

y

2

+y

4

=(x

2

+y

2

)

2

−x

2

y

2

=(x

2

+y

2

)

2

−(xy)

2

=(x

2

+y

2

+xy)(x

2

+y

2

−xy)

L.C.M. =(x+y)(x

2

−xy+y

2

)

(x−y)(x

2

+xy+y

2

)

=(x

3

+y

3

)(x

3

−y

3

)

=(x

3

)

2

−y

3

)

2

−x

6

−y

6