To find the product of the expression [tex]\((5x - 4)(-2x - 2)\)[/tex], let's proceed with the multiplication step by step:
1. Expand the Expression:
Let's multiply each term in the first binomial [tex]\((5x - 4)\)[/tex] by each term in the second binomial [tex]\((-2x - 2)\)[/tex].
[tex]\[
(5x - 4)(-2x - 2) = (5x)(-2x) + (5x)(-2) + (-4)(-2x) + (-4)(-2)
\][/tex]
2. Perform Individual Multiplications:
- [tex]\( (5x)(-2x) = -10x^2 \)[/tex]
- [tex]\( (5x)(-2) = -10x \)[/tex]
- [tex]\( (-4)(-2x) = 8x \)[/tex]
- [tex]\( (-4)(-2) = 8 \)[/tex]
3. Combine All the Terms:
Combine these results to form a single polynomial:
[tex]\[
-10x^2 - 10x + 8x + 8
\][/tex]
4. Simplify the Expression:
Combine like terms ([tex]\(-10x\)[/tex] and [tex]\(8x\)[/tex]):
[tex]\[
-10x^2 - 2x + 8
\][/tex]
Therefore, the expanded form of the expression [tex]\((5x - 4)(-2x - 2)\)[/tex] is [tex]\(-10x^2 - 2x + 8\)[/tex].
Now, let's compare this result with the given options:
1. [tex]\(-10x^2 + 8\)[/tex]
2. [tex]\(8x^2 - 25x + 3\)[/tex]
3. [tex]\(-10x^2 - 2x + 8\)[/tex]
4. [tex]\(8x^2 - 22x - 3\)[/tex]
The matching option is:
[tex]\[ \boxed{-10x^2 - 2x + 8} \][/tex]
Among the provided choices, this matches option 3 exactly.
Therefore, the correct answer is option 3.
