Answer :
Let's find the product of the two expressions [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] using the distributive property, which involves multiplying each term in the first expression by each term in the second expression.
Here are the steps:
1. Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex]
2. Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
- [tex]\((-2x) \times (-3) = 6x\)[/tex]
3. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex]
4. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex]
Now, we combine all these results, gathering like terms, if necessary:
- The result is: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
So, the correct answer is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Here are the steps:
1. Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex]
2. Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
- [tex]\((-2x) \times (-3) = 6x\)[/tex]
3. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex]
4. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex]
Now, we combine all these results, gathering like terms, if necessary:
- The result is: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
So, the correct answer is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
