please help. I am not sure if this is correct. I need to simplify this to the lowest terms
a^2 - 4b ^2
_____ ______
a+2b a+2b
my answer is:
a^2-4b^2
_________
a+2b
is this really to the lowest term?? for some reason I think I am doing this wrong. Thank you!
you are correct, as far as you have gone. However, since
a^2 - 4b^2 = (a-2b)(a+2b), you wind up with just
a-2b
12a^3b/-6ab^5
To simplify the expression (a^2 - 4b^2) / (a + 2b) to its lowest terms, you need to factor the numerator and the denominator.
First, let's factor the numerator:
a^2 - 4b^2 can be written as (a + 2b)(a - 2b).
Now, let's factor the denominator:
a + 2b doesn't have any common factors, so it cannot be simplified any further.
Now, we can rewrite the expression:
(a^2 - 4b^2) / (a + 2b) = [(a + 2b)(a - 2b)] / (a + 2b).
Notice that (a + 2b) appears in both the numerator and the denominator. This means it can be canceled out, leaving us with:
(a - 2b) / 1, which is simply (a - 2b).
Therefore, the simplified expression is a - 2b. It can't be simplified any further.
So, your answer is correct: a - 2b. Well done!