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Answer :
Sure! Let's go through the steps to find the product of [tex]\(\left(-2x - 9y^2\right)(-4x - 3)\)[/tex].
1. Distribute each term in the first polynomial by each term in the second polynomial:
- First, distribute [tex]\(-2x\)[/tex] to both [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
- Next, distribute [tex]\(-9y^2\)[/tex] to both [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
2. Combine all the terms together:
Putting all these products together, we get:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the correct product is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
From the provided answer choices, this matches with:
[tex]\( \boxed{8x^2 + 6x + 36xy^2 + 27y^2} \)[/tex]
1. Distribute each term in the first polynomial by each term in the second polynomial:
- First, distribute [tex]\(-2x\)[/tex] to both [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
- Next, distribute [tex]\(-9y^2\)[/tex] to both [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
2. Combine all the terms together:
Putting all these products together, we get:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the correct product is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
From the provided answer choices, this matches with:
[tex]\( \boxed{8x^2 + 6x + 36xy^2 + 27y^2} \)[/tex]
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