Answer :
To find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we will use the distributive property, which means we need to multiply each term in the first expression by each term in the second expression.
1. Multiply the first term of the first expression by each term in the second expression:
- 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. Multiply the second term of the first expression by each term in the second expression:
- 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 products obtained in steps 1 and 2:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Thus, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The result matches the third choice in the given list:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
1. Multiply the first term of the first expression by each term in the second expression:
- 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. Multiply the second term of the first expression by each term in the second expression:
- 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 products obtained in steps 1 and 2:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Thus, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The result matches the third choice in the given list:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
