Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answer box. Also, specify any restrictions on the variable.
6a^4+162a^3a^4−9a^3+27a^2
What you typed is not a rational expression, to have one I expect to see a fraction.
6a^4+162a/3a^4-9a^3+27a^2
6a^3*a+6*27a/3a^4-9a^3+27a^2
6a(a^3+27)/3a^4-9a^3+27a^2=
6a(a^3+27)/a^2(3a^2-9a+27)
I think you mean
6a(a^3+27)/(a^2(3a^2-9a+27)) or else only the a^2 is divided
= 6a(a^3+27)/(3a^2(a^2-3a+9))
= 6a(a+3)(a^2-3a+9) / (3a^2(a^2-3a+9))
= 6a(a+3) / (3a^2)
= 2(a+3)/a , a ≠ 0
To reduce a rational expression to its lowest terms, we need to simplify both the numerator and the denominator as much as possible. In this case, we have the rational expression:
(6a^4 + 162a^3a^4 − 9a^3 + 27a^2) / 1
First, let's factor out the common terms from the numerator:
6a^4 + 162a^3a^4 − 9a^3 + 27a^2 = 3a^2(2a^2 + 54a^3 − 3a + 9)
Now, let's factor further if possible. We can see that the expression inside the parentheses cannot be easily factored. Therefore, this rational expression cannot be simplified any further.
So, the rational expression in lowest terms is:
(2a^2 + 54a^3 − 3a + 9) / 1
There are no restrictions on the variable a since we did not encounter any denominator terms that could result in division by zero.