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How do you find the LCM for #y^3-y^2, y^4-y^2#?

Answer 1

Eva Abramson

The LCM = #y^4 -y^2 = y^2(y+1)(y-1)#

The first step is to factor each expression.

#y^3 - y^2 = color(white)(xxxxxxxx x)y^2(y-1)#

#y^4 - y^2 = y^2(y^2-1) = y^2(y+1)(y-1)#

The LCM is the product of the prime factors without any duplicates:

#y^3 -y^2# is a factor of #y^4 -y^2#

The LCM = #y^4 -y^2 = y^2(y+1)(y-1)#

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Answer 2

Jace Anderson

To find the least common multiple (LCM) for y^3-y^2 and y^4-y^2, we need to factorize both expressions.

For y^3-y^2, we can factor out y^2: y^3-y^2 = y^2(y-1).

For y^4-y^2, we can factor out y^2 as well: y^4-y^2 = y^2(y^2-1).

Now, we can see that both expressions have a common factor of y^2.

To find the LCM, we take the product of the highest powers of all the factors involved. In this case, the LCM is y^2(y-1)(y^2-1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.