Question

(a^4+4b^4)divided by (a^2-2ab+2b^2)

Answer 1

Simplify the following:
(a^4 + 4 b^4)/(a^2 - 2 a b + 2 b^2)
A common factor of a^4 + 4 b^4 and a^2 - 2 a b + 2 b^2 is a^2 - 2 a b + 2 b^2, so (a^4 + 4 b^4)/(a^2 - 2 a b + 2 b^2) = ((a^2 + 2 a b + 2 b^2) (a^2 - 2 a b + 2 b^2))/(a^2 - 2 a b + 2 b^2):((a^2 + 2 a b + 2 b^2) (a^2 - 2 a b + 2 b^2))/(a^2 - 2 a b + 2 b^2)
((a^2 + 2 a b + 2 b^2) (a^2 - 2 a b + 2 b^2))/(a^2 - 2 a b + 2 b^2) = (a^2 - 2 a b + 2 b^2)/(a^2 - 2 a b + 2 b^2)×(a^2 + 2 a b + 2 b^2) = a^2 + 2 a b + 2 b^2:
Answer:  a^2 + 2 a b + 2 b^2