Answer :
To find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we need to use the distributive property, which allows us to multiply each term in the first parentheses by each term in the second parentheses. Let's do this step-by-step:
1. Distribute [tex]\(-2x\)[/tex] to each term in [tex]\((-4x - 3)\)[/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] to each term in [tex]\((-4x - 3)\)[/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. Add all the results together:
Combine all the terms from the previous steps:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product of [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 36xy^2 + 6x + 27y^2
\][/tex]
This matches the option [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex], which is the correct answer.
1. Distribute [tex]\(-2x\)[/tex] to each term in [tex]\((-4x - 3)\)[/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] to each term in [tex]\((-4x - 3)\)[/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. Add all the results together:
Combine all the terms from the previous steps:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product of [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 36xy^2 + 6x + 27y^2
\][/tex]
This matches the option [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex], which is the correct answer.
