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

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Answer 1 · 2015-05-11T19:28:44

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#