Multiply:

To multiply, we will use distributive law as follows:

(2x2 − 1) by (4x3 + 5x2)

$=2 x^{2}\left(4 x^{3}+5 x^{2}\right)-1\left(4 x^{3}+5 x^{2}\right)$

$=8 x^{5}+10 x^{4}-4 x^{3}-5 x^{2}$

Thus, the answer is $8 x^{5}+10 x^{4}-4 x^{3}-5 x^{2}$.