Answer :
To find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], follow these steps:
1. Distribute Each Term in the First Parenthesis:
- Multiply [tex]\(-2x\)[/tex] by each term in the second parenthesis:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
- Multiply [tex]\(-9y^2\)[/tex] by each term in the second parenthesis:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
2. Combine All Product Terms:
- Now, bring all the products together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
3. Rearrange (If Necessary):
- Order the terms typically by decreasing powers of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is thus:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This matches one of the given answer choices, which is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
1. Distribute Each Term in the First Parenthesis:
- Multiply [tex]\(-2x\)[/tex] by each term in the second parenthesis:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
- Multiply [tex]\(-9y^2\)[/tex] by each term in the second parenthesis:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
2. Combine All Product Terms:
- Now, bring all the products together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
3. Rearrange (If Necessary):
- Order the terms typically by decreasing powers of [tex]\(x\)[/tex] and [tex]\(y\)[/tex]:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is thus:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This matches one of the given answer choices, which is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
