Question

How do you multiply `(6a^2-30a)/(a-2) * (a^2+2a-8)/(2a^3-10a^2)`?

Answer 1

The answer is : `(3a+12)/a`

Firstly, let's factor all the polynomials :

`(6a^(2)-30a)/(a-2) * (a^(2)+2a-8)/(2a^(3)-10a^(2)) = (6a(a-5))/(a-2) * ((a+4)(a-2))/(2a^(2)(a-5))`.

Now you can multiply the numerators together and then the denominators :

`(6a(a-5))/(a-2) * ((a+4)(a-2))/(2a^(2)(a-5))=(6a(a-5)(a+4)(a-2))/(2a^(2)(a-2)(a-5))`

Since the numerator and the denominator both have `a`, `(a-5)` and `(a-2)` in common, you can factor them out :

`(6a(a-5)(a+4)(a-2))/(2a^(2)(a-2)(a-5)) = (6*(a+4))/(2a)`

You can now divide 6 by 2 and calculate the answer :

`(6*(a+4))/(2a)=(3*(a+4))/(a)=(3a+12)/a=3+12/a`