Answer :
We begin with the expression
[tex]$$
\left(-2x - 9y^2\right)(-4x - 3).
$$[/tex]
To expand this product, we will use the distributive property, multiplying each term in the first parenthesis by each term in the second parenthesis.
1. Multiply the first term of the first parentheses by the first term of the second parentheses:
[tex]$$
(-2x) \cdot (-4x) = 8x^2.
$$[/tex]
2. Multiply the first term of the first parentheses by the second term of the second parentheses:
[tex]$$
(-2x) \cdot (-3) = 6x.
$$[/tex]
3. Multiply the second term of the first parentheses by the first term of the second parentheses:
[tex]$$
(-9y^2) \cdot (-4x) = 36xy^2.
$$[/tex]
4. Multiply the second term of the first parentheses by the second term of the second parentheses:
[tex]$$
(-9y^2) \cdot (-3) = 27y^2.
$$[/tex]
Now, add all these results together to obtain the expanded expression:
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
Thus, the correct expansion is
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
[tex]$$
\left(-2x - 9y^2\right)(-4x - 3).
$$[/tex]
To expand this product, we will use the distributive property, multiplying each term in the first parenthesis by each term in the second parenthesis.
1. Multiply the first term of the first parentheses by the first term of the second parentheses:
[tex]$$
(-2x) \cdot (-4x) = 8x^2.
$$[/tex]
2. Multiply the first term of the first parentheses by the second term of the second parentheses:
[tex]$$
(-2x) \cdot (-3) = 6x.
$$[/tex]
3. Multiply the second term of the first parentheses by the first term of the second parentheses:
[tex]$$
(-9y^2) \cdot (-4x) = 36xy^2.
$$[/tex]
4. Multiply the second term of the first parentheses by the second term of the second parentheses:
[tex]$$
(-9y^2) \cdot (-3) = 27y^2.
$$[/tex]
Now, add all these results together to obtain the expanded expression:
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
Thus, the correct expansion is
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
