Answer :
To find the product
$$
\left(-2x - 9y^2\right)\left(-4x - 3\right),
$$
we will use the distributive property (also known as the FOIL method when multiplying two binomials).
1. Multiply the first term in the first parenthesis by each term in the second parenthesis:
- $(-2x) \cdot (-4x) = 8x^2$,
- $(-2x) \cdot (-3) = 6x$.
2. Multiply the second term in the first parenthesis by each term in the second parenthesis:
- $(-9y^2) \cdot (-4x) = 36xy^2$,
- $(-9y^2) \cdot (-3) = 27y^2$.
3. Now, add up all the results:
$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$
Thus, the final expanded product is
$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$
$$
\left(-2x - 9y^2\right)\left(-4x - 3\right),
$$
we will use the distributive property (also known as the FOIL method when multiplying two binomials).
1. Multiply the first term in the first parenthesis by each term in the second parenthesis:
- $(-2x) \cdot (-4x) = 8x^2$,
- $(-2x) \cdot (-3) = 6x$.
2. Multiply the second term in the first parenthesis by each term in the second parenthesis:
- $(-9y^2) \cdot (-4x) = 36xy^2$,
- $(-9y^2) \cdot (-3) = 27y^2$.
3. Now, add up all the results:
$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$
Thus, the final expanded product is
$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$
