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Answer :
To solve the problem of finding the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], let's expand this expression step-by-step:
1. Distribute each term in the first binomial [tex]\((-2x - 9y^2)\)[/tex] to each term in the second binomial [tex]\((-4x - 3)\)[/tex].
2. Multiply [tex]\(-2x\)[/tex] with [tex]\(-4x\)[/tex]:
[tex]\[
-2x \times -4x = 8x^2
\][/tex]
3. Multiply [tex]\(-2x\)[/tex] with [tex]\(-3\)[/tex]:
[tex]\[
-2x \times -3 = 6x
\][/tex]
4. Multiply [tex]\(-9y^2\)[/tex] with [tex]\(-4x\)[/tex]:
[tex]\[
-9y^2 \times -4x = 36xy^2
\][/tex]
5. Multiply [tex]\(-9y^2\)[/tex] with [tex]\(-3\)[/tex]:
[tex]\[
-9y^2 \times -3 = 27y^2
\][/tex]
6. Combine all the products from the distribution:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This expanded expression is the product of the original binomials. Therefore, the answer is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This corresponds to one of the options provided:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
1. Distribute each term in the first binomial [tex]\((-2x - 9y^2)\)[/tex] to each term in the second binomial [tex]\((-4x - 3)\)[/tex].
2. Multiply [tex]\(-2x\)[/tex] with [tex]\(-4x\)[/tex]:
[tex]\[
-2x \times -4x = 8x^2
\][/tex]
3. Multiply [tex]\(-2x\)[/tex] with [tex]\(-3\)[/tex]:
[tex]\[
-2x \times -3 = 6x
\][/tex]
4. Multiply [tex]\(-9y^2\)[/tex] with [tex]\(-4x\)[/tex]:
[tex]\[
-9y^2 \times -4x = 36xy^2
\][/tex]
5. Multiply [tex]\(-9y^2\)[/tex] with [tex]\(-3\)[/tex]:
[tex]\[
-9y^2 \times -3 = 27y^2
\][/tex]
6. Combine all the products from the distribution:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This expanded expression is the product of the original binomials. Therefore, the answer is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This corresponds to one of the options provided:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
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