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Answer :
To solve the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we need to use the distributive property to expand it. Here's a step-by-step breakdown:
1. Distribute each term in the first parenthesis to each term in the second parenthesis:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
2. Combine all the results to form the expanded expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the expanded product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This corresponds to the option:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
1. Distribute each term in the first parenthesis to each term in the second parenthesis:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
2. Combine all the results to form the expanded expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the expanded product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This corresponds to the option:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
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