Question

Find the LCM of
4(x²-y²) ,6(x³-y³) and 9(x³+y³)

Solution: Here, 1st Polynomial 4(x²-y²) = 2²(x+y) (x-y)
2nd polynomial
6(x³-y³) = 2x3(x-y) (x²-xy+y²)
3rd Polynomial
9(x³+y³)= 3²(x+y) (x²-xy+y²)

Now, LCM of the polynomial
=2²x3²(x+y)(x-y) (x+y) (x²-xy+y²)
= 36(x²-y²) (x³+y³)
=36 (x²)³ - )(y²)³
=36(x⁶- y⁶)
hence proved​

Answer 1

Step-by-step explanation:

Solution: Here, 1st Polynomial 4(x²-y²) = 2²(x+y) (x-y)

2nd polynomial

2nd polynomial6(x³-y³) = 2x3(x-y) (x²-xy+y²)

2nd polynomial6(x³-y³) = 2x3(x-y) (x²-xy+y²) 3rd Polynomial

2nd polynomial6(x³-y³) = 2x3(x-y) (x²-xy+y²) 3rd Polynomial9(x³+y³)= 3²(x+y) (x²-xy+y²)

Now, LCM of the polynomial

Now, LCM of the polynomial=2²x3²(x+y)(x-y) (x+y) (x²-xy+y²)

Now, LCM of the polynomial=2²x3²(x+y)(x-y) (x+y) (x²-xy+y²) = 36(x²-y²) (x³+y³)

Now, LCM of the polynomial=2²x3²(x+y)(x-y) (x+y) (x²-xy+y²) = 36(x²-y²) (x³+y³)=36 (x²)³ - )(y²)³

Now, LCM of the polynomial=2²x3²(x+y)(x-y) (x+y) (x²-xy+y²) = 36(x²-y²) (x³+y³)=36 (x²)³ - )(y²)³=36(x⁶- y⁶)

Now, LCM of the polynomial=2²x3²(x+y)(x-y) (x+y) (x²-xy+y²) = 36(x²-y²) (x³+y³)=36 (x²)³ - )(y²)³=36(x⁶- y⁶)hence proved

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