Answer :
To find the product of
$$
(-2x-9y^2)(-4x-3),
$$
we will use the distributive property (also known as the FOIL method for binomials).
1. Multiply the first terms:
$$(-2x) \cdot (-4x) = 8x^2.$$
2. Multiply the outer terms:
$$(-2x) \cdot (-3) = 6x.$$
3. Multiply the inner terms:
$$(-9y^2) \cdot (-4x) = 36xy^2.$$
4. Multiply the last terms:
$$(-9y^2) \cdot (-3) = 27y^2.$$
Now, add all these results together:
$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$
Thus, the product is:
$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$
Comparing this with the multiple choice options, the correct answer is option 3.
$$
(-2x-9y^2)(-4x-3),
$$
we will use the distributive property (also known as the FOIL method for binomials).
1. Multiply the first terms:
$$(-2x) \cdot (-4x) = 8x^2.$$
2. Multiply the outer terms:
$$(-2x) \cdot (-3) = 6x.$$
3. Multiply the inner terms:
$$(-9y^2) \cdot (-4x) = 36xy^2.$$
4. Multiply the last terms:
$$(-9y^2) \cdot (-3) = 27y^2.$$
Now, add all these results together:
$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$
Thus, the product is:
$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$
Comparing this with the multiple choice options, the correct answer is option 3.
