The problem asks us to expand the expression $(4a+b)(5a-3b)$.

1. Problem Description

The problem asks us to expand the expression $(4a+b)(5a-3b)$.

2. Solution Steps

We need to multiply each term in the first parenthesis by each term in the second parenthesis.

$(4a+b)(5a-3b)$

$= 4a(5a-3b) + b(5a-3b)$

$= (4a)(5a) + (4a)(-3b) + (b)(5a) + (b)(-3b)$

$= 20a^2 -12ab + 5ab -3b^2$

Now we combine the like terms: $-12ab$ and $5ab$.

$-12ab + 5ab = -7ab$

So the expression becomes:

$20a^2 -7ab -3b^2$

3. Final Answer

$20a^2 - 7ab - 3b^2$