I'm totally stuck on this problem!!
Simplify:
(2a^2+13a-7/3a^3-27a)(4a^2-1/9a^2)
This probably should have been written as
(2a^2+13a-7)/[(3a^3-27a)(4a^2-1)/9a^2]
Try factoring 2a^2 +13a -7 into
(2a -1)(a+7)
and 3a^3-27a into
3a(a^2-9 = 3a(a+3)(a-3)
and 4a^2 -1 into (2a +1) (2a -1)
The 3a and (2a-1) terms will cancel.
No,
I'm sure the problem is written like this:
[(3a^3-27a)/(2a^2+13a-7)]/[9a^2/4a^2-1)]
And to divide you multiply by the reciprocal.
So i still don't get the problem I also know to factor, but I'm stil confused.
What you just typed as sure as the problem as written is NOT close to what you posted. Factor, then divide out common factors.
To simplify the expression (2a^2+13a-7/3a^3-27a)(4a^2-1/9a^2), we can start by simplifying each term separately.
First, let's simplify the numerator:
2a^2 + 13a - 7
Next, let's simplify the denominator:
3a^3 - 27a = 3a(a^2 - 9) = 3a(a-3)(a+3)
Now, let's simplify the term in parentheses:
4a^2 - 1/9a^2 = 4a^2 - (1/9)a^2 = (36a^2 - 1)/9a^2
Now, let's substitute these simplified expressions back into the original expression:
(2a^2 + 13a - 7)/(3a(a-3)(a+3)) * (36a^2 - 1)/9a^2
Now, we can combine the two fractions by multiplying their numerators together and their denominators together:
(2a^2 + 13a - 7)(36a^2 - 1) / (3a(a-3)(a+3) * 9a^2)
Now, we can expand the numerator and cancel out common factors:
(72a^4 + 468a^3 - 72a^2 - 468a - 36a^2 + 234 - 72a^2 + 468a - 72) / (27a^3(a-3)(a+3))
Simplifying further:
(72a^4 - 180a^2 + 162) / (27a^3(a-3)(a+3))
And finally, we can simplify the numerator as much as possible:
18(4a^4 - 10a^2 + 9) / (27a^3(a-3)(a+3))
Therefore, the simplified expression is:
(18(4a^4 - 10a^2 + 9)) / (27a^3(a-3)(a+3))