Answer :
To solve the product [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we need to use the distributive property (also known as the FOIL method for binomials):
1. Distribute [tex]\(-2x\)[/tex] to each term in the second binomial [tex]\((-4x - 3)\)[/tex]:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
2. Distribute [tex]\(-9y^2\)[/tex] to each term in the second binomial [tex]\((-4x - 3)\)[/tex]:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
3. Combine all the resulting terms:
- [tex]\(8x^2\)[/tex] from the first multiplication.
- [tex]\(6x\)[/tex] from the second multiplication.
- [tex]\(36xy^2\)[/tex] from the third multiplication.
- [tex]\(27y^2\)[/tex] from the fourth multiplication.
When we bring all these terms together, we get:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
This matches the answer option [tex]\(\boxed{8x^2 + 6x + 36xy^2 + 27y^2}\)[/tex].
1. Distribute [tex]\(-2x\)[/tex] to each term in the second binomial [tex]\((-4x - 3)\)[/tex]:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
2. Distribute [tex]\(-9y^2\)[/tex] to each term in the second binomial [tex]\((-4x - 3)\)[/tex]:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
3. Combine all the resulting terms:
- [tex]\(8x^2\)[/tex] from the first multiplication.
- [tex]\(6x\)[/tex] from the second multiplication.
- [tex]\(36xy^2\)[/tex] from the third multiplication.
- [tex]\(27y^2\)[/tex] from the fourth multiplication.
When we bring all these terms together, we get:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
This matches the answer option [tex]\(\boxed{8x^2 + 6x + 36xy^2 + 27y^2}\)[/tex].
