Simplify: `a^2b(a-b^2)+a b^2(4a b-2a^2)-a^3b(1-2b)`

Explanation

To simplify the expression \( a^2b(a - b^2) + ab^2(4ab - 2a^2) - a^3b(1 - 2b) \), we will follow these steps:

### Step 1: Expand Each Term
We will start by expanding each term in the expression.

1. **First term**: \( a^2b(a - b^2) = a^2b \cdot a - a^2b \cdot b^2 = a^3b - a^2b^3 \)
2. **Second term**: \( ab^2(4ab - 2a^2) = ab^2 \cdot 4ab - ab^2 \cdot 2a^2 = 4a^2b^3 - 2a^3b^2 \)
3. **Third term**: \( -a^3b(1 - 2b) = -a^3b \cdot 1 + a^3b \cdot 2b = -a^3b + 2a^3b^2 \)
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