Answer :
To find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we will use the distributive property, also known as the FOIL method (First, Outside, Inside, Last), since we have two binomials:
1. Distribute [tex]\(-2x\)[/tex]:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
-2x \times -4x = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-2x \times -3 = 6x
\][/tex]
2. Distribute [tex]\(-9y^2\)[/tex]:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
-9y^2 \times -4x = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-9y^2 \times -3 = 27y^2
\][/tex]
3. Combine all the results:
- Add all the products together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the final expanded product is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Looking at the provided answer choices, the correct one is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
1. Distribute [tex]\(-2x\)[/tex]:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
-2x \times -4x = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-2x \times -3 = 6x
\][/tex]
2. Distribute [tex]\(-9y^2\)[/tex]:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
-9y^2 \times -4x = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-9y^2 \times -3 = 27y^2
\][/tex]
3. Combine all the results:
- Add all the products together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the final expanded product is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Looking at the provided answer choices, the correct one is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
