Answer :
We want to multiply
[tex]$$
\left(-2x - 9y^2\right) \left(-4x - 3\right).
$$[/tex]
To do this, we use the distributive property by multiplying each term in the first factor by each term in the second factor.
1. Multiply the first terms:
[tex]$$
(-2x) \cdot (-4x) = 8x^2.
$$[/tex]
2. Multiply the outer terms:
[tex]$$
(-2x) \cdot (-3) = 6x.
$$[/tex]
3. Multiply the inner terms:
[tex]$$
(-9y^2) \cdot (-4x) = 36xy^2.
$$[/tex]
4. Multiply the last terms:
[tex]$$
(-9y^2) \cdot (-3) = 27y^2.
$$[/tex]
Now, add all the products together:
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
Thus, the final product is
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
[tex]$$
\left(-2x - 9y^2\right) \left(-4x - 3\right).
$$[/tex]
To do this, we use the distributive property by multiplying each term in the first factor by each term in the second factor.
1. Multiply the first terms:
[tex]$$
(-2x) \cdot (-4x) = 8x^2.
$$[/tex]
2. Multiply the outer terms:
[tex]$$
(-2x) \cdot (-3) = 6x.
$$[/tex]
3. Multiply the inner terms:
[tex]$$
(-9y^2) \cdot (-4x) = 36xy^2.
$$[/tex]
4. Multiply the last terms:
[tex]$$
(-9y^2) \cdot (-3) = 27y^2.
$$[/tex]
Now, add all the products together:
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
Thus, the final product is
[tex]$$
8x^2 + 6x + 36xy^2 + 27y^2.
$$[/tex]
