Question

Simplify each expression
(a^3-2a^2)-(3a^2-4a^3)

Answer 1

To simplify the expression \((a^3 - 2a^2) - (3a^2 - 4a^3)\), we will first distribute the negative sign across the second set of parentheses:

\[
(a^3 - 2a^2) - (3a^2 - 4a^3) = a^3 - 2a^2 - 3a^2 + 4a^3
\]

Next, we combine like terms. The like terms are \(a^3\) and \(4a^3\), as well as \(-2a^2\) and \(-3a^2\):

1. Combine \(a^3\) and \(4a^3\):
\[
a^3 + 4a^3 = 5a^3
\]

2. Combine \(-2a^2\) and \(-3a^2\):
\[
-2a^2 - 3a^2 = -5a^2
\]

Putting it all together, the simplified expression is:

\[
5a^3 - 5a^2
\]

We can factor out a common term of \(5a^2\):

\[
5a^2(a - 1)
\]

Thus, the final simplified expression is:

\[
5a^2(a - 1)
\]