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Answer :
To find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we will follow these steps to multiply the expressions:
1. Use the distributive property: This property lets us multiply each term in the first parentheses by each term in the second.
2. Multiply each pair of terms:
- First, multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
- Next, multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
- Then, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
- Finally, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
3. Add all the results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(\boxed{8x^2 + 6x + 36xy^2 + 27y^2}\)[/tex].
1. Use the distributive property: This property lets us multiply each term in the first parentheses by each term in the second.
2. Multiply each pair of terms:
- First, multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
- Next, multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
- Then, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
- Finally, multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
3. Add all the results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(\boxed{8x^2 + 6x + 36xy^2 + 27y^2}\)[/tex].
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