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Answer :
Let's find the product of the given expressions: [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
To multiply these two expressions together, you will apply the distributive property, often referred to as FOIL (First, Outside, Inside, Last) for binomials.
1. First Terms: Multiply the first terms of each binomial:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
2. Outside Terms: Multiply the outer terms of the binomials:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
3. Inside Terms: Multiply the inner terms of the binomials:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
4. Last Terms: Multiply the last terms of each binomial:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
Now, combine all the results:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] simplifies to:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Among the given choices, this matches:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, this is the correct product of the expressions.
To multiply these two expressions together, you will apply the distributive property, often referred to as FOIL (First, Outside, Inside, Last) for binomials.
1. First Terms: Multiply the first terms of each binomial:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
2. Outside Terms: Multiply the outer terms of the binomials:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
3. Inside Terms: Multiply the inner terms of the binomials:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
4. Last Terms: Multiply the last terms of each binomial:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
Now, combine all the results:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] simplifies to:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Among the given choices, this matches:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, this is the correct product of the expressions.
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