x³-2x²y +2xy² -y³, x⁴ -y⁴, x³ +y³ | Find the LCM | SciPiPupil

Question: Find the LCM between x³ -2x²y +2xy² -y³, x⁴ -y⁴, and x³ +y³.

Solution:

Given,

1st expression: x³ -2x²y +2xy² -y³

= x³ -y³ - 2xy (x -y)

= (x -y)(x² +xy +y²) - 2xy (x-y)

= (x -y)(x² +xy -2xy +y²)

= (x -y)(x² -xy +y²)

2nd expression: x⁴ -y⁴

= (x²)² - (y²)²

= (x² +y²)(x² -y²)

= (x² +y²)(x+y)(x-y)

= (x+y)(x-y)(x² +y²)

3rd expression: x³ +y³

= (x+y)(x² -xy +y²)

Now,

Lowest Common Multiples (L.C.M.) = (x+y)(x-y)(x²-xy+y²) * (x² +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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