Answer :
Sure! Let's solve the problem step-by-step by expanding the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
### Step 1: Distribute each term from the first expression to each term in the second expression.
1. Distribute [tex]\(-2x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
2. Distribute [tex]\(-9y^2\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
### Step 2: Combine all the terms together.
Now, we'll add all the results from the distribution:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This is the expanded form of the product.
### Conclusion
The expanded product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This corresponds to the option:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
### Step 1: Distribute each term from the first expression to each term in the second expression.
1. Distribute [tex]\(-2x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
2. Distribute [tex]\(-9y^2\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
### Step 2: Combine all the terms together.
Now, we'll add all the results from the distribution:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This is the expanded form of the product.
### Conclusion
The expanded product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This corresponds to the option:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
