How do you factor #5a^2 + 10ab - 40b^2#?

1 Answer
Konstantinos Michailidis
Sep 10, 2015

One way of doing it is in the explanation

Explanation:

Hence we have that

#5a^2+10ab-40b^2=> 5(a^2+2ab+b^2)-45b^2=> 5(a+b)^2-(sqrt45b)^2=> (sqrt5(a+b))^2-(sqrt45*b)^2=> (sqrt5*(a+b)+sqrt45*b))*(sqrt5*(a+b)-sqrt45b)#

Or noticing that #sqrt(45)=sqrt(9*5)=3*sqrt5#

we get that

#5a^2+10ab-40b^2=5*(a+4b)*(a-2b)#

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