Simplify the expression \(\frac{a^2 b^4 - b^2 a^4}{ab(a + b)}\)
A
\(a^2 - b^2\)
B
\(b^2 - a^2\)
C
\(a^2b - ab^2\)
D
\(ab^2 - a^2b\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{a^2 b^4 - b^2 a^4}{ab(a + b)}\) = \(\frac{a^2 b^2(b^2 - a^2)}{ab(a + b)}\)
= \(\frac{ab [(b - a) (b + a)]}{a + b}\)
= ab(b - a)
= \(ab^2 - a^2b\)
Source: Myschool Past Questions Archive (Record #50112)