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What is the product of [tex](-2x-9y^2)(-4x-3)[/tex]?

A. [tex]-8x^2 - 6x - 36xy^2 - 27y^2[/tex]
B. [tex]-14x^2 - 36xy^2 + 27y^2[/tex]
C. [tex]8x^2 + 6x + 36xy^2 + 27y^2[/tex]
D. [tex]14x^2 + 36xy^2 + 27y^2[/tex]

Answer :

Let's solve the problem step by step by expanding the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] using the distributive property, also known as the FOIL method (First, Outer, Inner, Last):

1. First: Multiply the first terms of each binomial.
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]

2. Outer: Multiply the outer terms.
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]

3. Inner: Multiply the inner terms.
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]

4. Last: Multiply the last terms of each binomial.
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]

Next, add all these results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]

So, the expanded expression is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]. This matches the third option in the list provided.

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