Question

Find LCM x⁴-y⁴,x²-y² and x³-y³​

Answer 1

Answer:

Step-by-step explanation:

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)