How do you factor 5a^2 + 10ab - 40b^25a2+10ab40b2?

1 Answer

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)