4a^2/(a-b)- (4b^2-8ab)/(b-a) I have the answe as 4(a-b) is this correct?

subtract and simplify: 4a^2/(a-b)- (4b^2-8ab)/(b-a) I have the answe

Yes

Thanks

To subtract and simplify the given expression:

4a^2/(a-b) - (4b^2-8ab)/(b-a)

First, let's simplify each fraction separately:
4a^2/(a-b) can be left as is since it cannot be simplified further.

For (4b^2-8ab)/(b-a), we can factor out a common factor of 4:
4(b^2-2ab)/(b-a)

Now, notice that (b^2-2ab) can be factored further:
b(b-2a)/(b-a)

By cancelling out the common factor of (b-a), we get:
b(b-2a)/(b-a) = b

Now, we can rewrite the original expression using the simplified fractions:
4a^2/(a-b) - (4b^2-8ab)/(b-a) = 4a^2/(a-b) - b

To combine the fractions, we need a common denominator. In this case, the common denominator is (a-b). Therefore, we need to multiply the numerator and denominator of the first fraction by (b-a):
[4a^2 * (b-a)]/[(a-b)*(b-a)] - b(a-b)/(a-b)

Simplifying further:
[4a^2b-4a^3 - ab(a-b)]/[(a-b)*(b-a)] - b(a-b)/(a-b)
= (4a^2b-4a^3 - ab^2+ab)/(a^2-2ab+b^2) - 1

Now, we combine the terms in the numerator:
= 4a^2b - 4a^3 - ab^2 + ab - 1

Hence, the simplified expression is:
4a^2b - 4a^3 - ab^2 + ab - 1.