Answer
$ 4a^3b^3-a^4b^2.$
Work Step by Step
By multiplying each term of the polynomial by the factor $\frac{1}{2}a^2b$, and then adding the products, we have
$$
\frac{1}{2}a^2b(8ab^2 - 2a^2b)=\frac{1}{2}a^2b(8ab^2)+ \frac{1}{2}a^2b(- 2a^2b)\\
= 4a^3b^3-a^4b^2.
$$
