The problem asks to multiply and simplify the expression $-7\sqrt{a}(\sqrt{3b} + 5\sqrt{6})$. It is assumed that all variables represent non-negative numbers.

1. Problem Description

The problem asks to multiply and simplify the expression $-7\sqrt{a}(\sqrt{3b} + 5\sqrt{6})$. It is assumed that all variables represent non-negative numbers.

2. Solution Steps

First, distribute the term $-7\sqrt{a}$ to both terms inside the parentheses:

$-7\sqrt{a}(\sqrt{3b} + 5\sqrt{6}) = -7\sqrt{a}\sqrt{3b} - 7\sqrt{a}(5\sqrt{6})$

Next, simplify each term:

$-7\sqrt{a}\sqrt{3b} = -7\sqrt{3ab}$

$-7\sqrt{a}(5\sqrt{6}) = -35\sqrt{6a}$

Combine the simplified terms:

$-7\sqrt{3ab} - 35\sqrt{6a}$

3. Final Answer

$-7\sqrt{3ab} - 35\sqrt{6a}$