Answer :

To simplify the expression [tex]\(-10(-2y - 4)\)[/tex] using the distributive property, follow these steps:

1. Identify the Distributive Property:
The distributive property states that [tex]\(a(b + c) = ab + ac\)[/tex]. In this case, we will distribute [tex]\(-10\)[/tex] across [tex]\(-2y - 4\)[/tex].

2. Apply the Distributive Property:
Distribute [tex]\(-10\)[/tex] to each term inside the parentheses:
[tex]\[ -10(-2y) + (-10)(-4) \][/tex]

3. Simplify Each Term:
- For the first term, [tex]\(-10 \times -2y\)[/tex]:
[tex]\[ -10 \times -2y = 20y \][/tex]
- For the second term, [tex]\(-10 \times -4\)[/tex]:
[tex]\[ -10 \times -4 = 40 \][/tex]

4. Combine the Results:
Combine the simplified terms:
[tex]\[ 20y + 40 \][/tex]

Therefore, using the distributive property, the simplified form of [tex]\(-10(-2y - 4)\)[/tex] is:
[tex]\[ -10(-2y - 4) = 20y + 40 \][/tex]

So in the equation:
[tex]\[ -10(-2y - 4) = [?]y + \square \][/tex]

The values for the blanks are:
[tex]\[ [?] = 20 \quad \text{and} \quad \square = 40 \][/tex]

Hence, the solution is:
[tex]\[ -10(-2y - 4) = 20y + 40 \][/tex]