Multiply: (0.8a − 0.5b) by (1.5a − 3b)

To multiply, we will use distributive law as follows:

(0.8a − 0.5b) by (1.5a − 3b)

$=0.8 a(1.5 a-3 b)-0.5 b(1.5 a-3 b)$

$=1.2 a^{2}-2.4 a b-0.75 a b+1.5 b^{2}$

$=1.2 a^{2}-3.15 a b+1.5 b^{2}$

Thus, the answer is $1.2 a^{2}-3.15 a b+1.5 b^{2}$.