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Answer :
Sure! Let's solve the given expression step-by-step:
We need to find the product of the two expressions [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex].
1. Distribute each term from the first expression to the second expression:
- Multiply [tex]\(-2x\)[/tex] by each term in the second expression:
- [tex]\((-2x) \cdot (-4x) = 8x^2\)[/tex]
- [tex]\((-2x) \cdot (-3) = 6x\)[/tex]
- Multiply [tex]\(-9y^2\)[/tex] by each term in the second expression:
- [tex]\((-9y^2) \cdot (-4x) = 36xy^2\)[/tex]
- [tex]\((-9y^2) \cdot (-3) = 27y^2\)[/tex]
2. Add all these products together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This is the simplified expression after multiplying.
So, the correct choice from the given options is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
We need to find the product of the two expressions [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex].
1. Distribute each term from the first expression to the second expression:
- Multiply [tex]\(-2x\)[/tex] by each term in the second expression:
- [tex]\((-2x) \cdot (-4x) = 8x^2\)[/tex]
- [tex]\((-2x) \cdot (-3) = 6x\)[/tex]
- Multiply [tex]\(-9y^2\)[/tex] by each term in the second expression:
- [tex]\((-9y^2) \cdot (-4x) = 36xy^2\)[/tex]
- [tex]\((-9y^2) \cdot (-3) = 27y^2\)[/tex]
2. Add all these products together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This is the simplified expression after multiplying.
So, the correct choice from the given options is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
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