x⁴ +x²y² +y⁴, and x³ -y³ | Find the LCM | SciPiPupil

Question: Find the L.C.M. between x⁴ +x²y² +y⁴ and x³ -y³.

Solution:

Given,

1st expression: x⁴ +x²y² +y⁴

= (x⁴ +y⁴) + x²y²

= (x²)² + (y²)² + x²y²

= (x² +y²) - 2x²y² +x²y²

= (x² +y²) - x²y²

= (x² +y²) - (xy)²

= (x² +xy +y²) (x² -xy +y²)

2nd expression: x³ -y³

= (x-y)(x²+xy+y²)

Now,

Lowest Common Multiples (LCM) = common factors* rest factors

= (x² +xy +y²) * (x-y)(x² -xy +y²)

= (x² -xy +y²) (x-y)(x²+xy+y²)

= (x² -xy +y²) (x³ -y³)

Related Notes and Solutions:

Here is the Website link to the guide of solving HCF and LCM.

Here are all solutions of LCM for Class 10.

#SciPiPupil