Subtract and Simplify:

4a^2/(a-b)-(4b^2-8ab)/(b-a)
I have the answer as 4(a+b)^2/(a-b)

or should it be 4(a-b)^2/(a-b)

Responses

Math problem check - bobpursley, Sunday, October 12, 2008 at 4:23pm

just the numerator..

4a^2-8ab + 4b^2, right?
4(a-b)^2

Now does that reduce with the denominator?



Math problem check - Shawn, Sunday, October 12, 2008 at 4:28pm
Okay I have the answer as 4(a-b) is that right

Math problem check - Shawn, Sunday, October 12, 2008 at 4:37pm
What about
4a^2/(a-b)-(4b^2-8ab)/(b-a)
I thought that you would multiple the second part of the equation by -1
-(4b^2-8ab)/(b-a)
to get the common LCD of a-b
So I thought the equation would be 4a^2/(a-b) + (4b^2 + 8ab)/(a-b)

I have the answer as 4(a+b)^2/(a-b)

You are wrong.

THe second part only..

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

Your answer is still wrong.

To solve the given expression, let's take it step by step:

First, let's look at the numerator of the expression: 4a^2/(a-b) - (4b^2-8ab)/(b-a)

To subtract these fractions, we need a common denominator.
The common denominator in this case is (a-b)(b-a) = -(a-b)^2.

Now, let's rewrite the expression with the common denominator:

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

Simplifying the numerator of the first fraction, we have:

(4a^2 * (b-a)) = 4a^2b - 4a^3

Now, let's rewrite the expression:

(4a^2b - 4a^3)/(-(a-b)^2) - (4b^2-8ab)/(b-a)

Now, let's simplify the second numerator:

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

Rewriting the expression again:

(4a^2b - 4a^3)/(-(a-b)^2) - 4b(b-2a)/(b-a)

Now, let's combine the two fractions:

[(4a^2b - 4a^3) - 4b(b-2a)] / (-(a-b)^2 * (b-a))

Simplifying the numerator further:

(4a^2b - 4a^3 - 4b^2 + 8ab) / (-(a-b)^2 * (b-a))

Combining like terms in the numerator:

(4a^2b + 8ab - 4a^3 - 4b^2) / (-(a-b)^2 * (b-a))

Now, let's factor out common terms in the numerator:

4ab(a + 2 - a^2/b) / (-(a-b)^2 * (b-a))

At this point, it seems there might be some confusion in the responses you provided. Some of the suggested answers do not match the simplification we have done so far.

If you would like further clarification or explanation, please let me know.