Answer :
To find the product
$$
\left(-2x-9y^2\right)(-4x-3),
$$
we use the distributive property (also known as the FOIL method when multiplying two binomials). Here are the steps:
1. Multiply the first term in the first expression by the first term in the second expression:
$$
(-2x) \cdot (-4x) = 8x^2.
$$
2. Multiply the first term in the first expression by the second term in the second expression:
$$
(-2x) \cdot (-3) = 6x.
$$
3. Multiply the second term in the first expression by the first term in the second expression:
$$
(-9y^2) \cdot (-4x) = 36xy^2.
$$
4. Multiply the second term in the first expression by the second term in the second expression:
$$
(-9y^2) \cdot (-3) = 27y^2.
$$
After calculating these four products, add them together:
$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$
Thus, the product is
$$
8x^2+6x+36xy^2+27y^2.
$$
$$
\left(-2x-9y^2\right)(-4x-3),
$$
we use the distributive property (also known as the FOIL method when multiplying two binomials). Here are the steps:
1. Multiply the first term in the first expression by the first term in the second expression:
$$
(-2x) \cdot (-4x) = 8x^2.
$$
2. Multiply the first term in the first expression by the second term in the second expression:
$$
(-2x) \cdot (-3) = 6x.
$$
3. Multiply the second term in the first expression by the first term in the second expression:
$$
(-9y^2) \cdot (-4x) = 36xy^2.
$$
4. Multiply the second term in the first expression by the second term in the second expression:
$$
(-9y^2) \cdot (-3) = 27y^2.
$$
After calculating these four products, add them together:
$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$
Thus, the product is
$$
8x^2+6x+36xy^2+27y^2.
$$
