Answer :
Let's find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] by expanding it step by step.
1. Distribute each term in the first parenthesis to each term in the second parenthesis:
- 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]
- 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]
2. Combine all the terms we've found:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the expanded form of the expression is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
The correct answer is the option [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
1. Distribute each term in the first parenthesis to each term in the second parenthesis:
- 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]
- 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]
2. Combine all the terms we've found:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the expanded form of the expression is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
The correct answer is the option [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
