x⁴-y⁴, x²-y², and x³-y³ | Find the LCM | SciPiPupil

Question: Find the LCM between x⁴-y⁴, x²-y², and x³-y³.

Solution:

Given,

1st expression: x⁴-y⁴

= (x²)² - (y²)²

= (x² +y²)(x² -y²)

= (x² +y²)(x +y)(x -y)

= (x +y)(x -y)(x² +y²)

2nd expression: x² -y²

= (x +y)(x -y)

3rd expression: x³ -y³

= (x -y)(x² +xy +y²)

Now,

Lowest Common Multiples (L.C.M.) = common factors * rest factors

= (x+y)(x-y) * (x² +y²)(x² +xy +y²)

= (x² -y²)(x²+y²) * (x² +xy +y²)

= (x⁴ -y⁴)(x² +xy +y²)

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.

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