To simplify the given expression:
[tex]\[
-\left(4a^2 b^3 - 4a^3 b^5\right) - a^2 b^3
\][/tex]
we need to follow these steps:
### Step 1: Distribute the negative sign inside the brackets
First, let's distribute the negative sign inside the brackets:
[tex]\[
- (4a^2 b^3) + 4a^3 b^5 - a^2 b^3
\][/tex]
### Step 2: Combine like terms
Next, combine the like terms:
[tex]\[
-4a^2 b^3 - a^2 b^3 + 4a^3 b^5
\][/tex]
### Step 3: Add and subtract the like terms
Combine [tex]\(-4a^2 b^3\)[/tex] and [tex]\(-a^2 b^3\)[/tex]:
[tex]\[
-4a^2 b^3 - a^2 b^3 = -5a^2 b^3
\][/tex]
So the expression now is:
[tex]\[
-5a^2 b^3 + 4a^3 b^5
\][/tex]
### Step 4: Factor the expression
Factor the common term [tex]\((a^2 b^3)\)[/tex] out of the two terms:
[tex]\[
-5a^2 b^3 + 4a^3 b^5 = a^2 b^3 (-5 + 4a b^2)
\][/tex]
Restate it in a simplified factorized form:
[tex]\[
a^2 b^3 (4a b^2 - 5)
\][/tex]
### Conclusion:
Therefore, the simplified form of the given expression is:
[tex]\[
a^2 b^3 (4a b^2 - 5)
\][/tex]
