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 :

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

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