Simplify the expression \(\frac{a^2 b^4 - b^2 a^4}{ab(a + b)}\)
Question 1 Report
Simplify the expression \(\frac{a^2 b^4 - b^2 a^4}{ab(a + b)}\)
Answer Details
The expression can be simplified as follows:
First, we can factor out the common factor of \(ab\) from the numerator:
\begin{align*}
\frac{a^2 b^4 - b^2 a^4}{ab(a + b)} &= \frac{ab(a^2 b^3 - b^2 a^3)}{ab(a + b)} \\
&= \frac{ab(a^2 b^3 - b^2 a^3)}{ab(a + b)} \\
&= \frac{a^2 b^3 - b^2 a^3}{a + b}.
\end{align*}
Next, we can simplify the numerator:
\begin{align*}
a^2 b^3 - b^2 a^3 &= (a^2)(b^3) - (b^2)(a^3) \\
&= a^2b^2 (b - a) \\
&= ab^2 (a - b)(b + a) \\
&= ab^2 (a^2 - b^2).
\end{align*}
Therefore, the expression simplifies to:
\[\frac{ab^2 (a^2 - b^2)}{a + b} = ab (a - b) = \boxed{ab^2 - a^2b}.\]
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