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Answer :
To find the product of [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex], we'll distribute each term in the first binomial to each term in the second binomial. Let's do this step-by-step:
1. Distribute [tex]\(-2x\)[/tex] to [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex]:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
2. Distribute [tex]\(-9y^2\)[/tex] to [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex]:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
3. Combine all the results from the distributions:
The resulting expression from all the terms calculated above is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the following given choice:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
1. Distribute [tex]\(-2x\)[/tex] to [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex]:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
2. Distribute [tex]\(-9y^2\)[/tex] to [tex]\(-4x\)[/tex] and [tex]\(-3\)[/tex]:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
3. Combine all the results from the distributions:
The resulting expression from all the terms calculated above is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the following given choice:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
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