Answer :
To find the product [tex]\((-2x-9y^2)(-4x-3)\)[/tex], we'll multiply each term in the first expression by each term in the second expression. Let's go through this step-by-step:
1. Multiply the First Terms:
- Take the [tex]\(-2x\)[/tex] from the first expression and multiply it by the [tex]\(-4x\)[/tex] from the second expression:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Multiply the Outer Terms:
- Take [tex]\(-2x\)[/tex] from the first expression and multiply it by the [tex]\(-3\)[/tex] from the second expression:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Multiply the Inner Terms:
- Take [tex]\(-9y^2\)[/tex] from the first expression and multiply it by the [tex]\(-4x\)[/tex] from the second expression:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Multiply the Last Terms:
- Take [tex]\(-9y^2\)[/tex] from the first expression and multiply it by the [tex]\(-3\)[/tex] from the second expression:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Finally, combine all these results to write the complete polynomial:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Hence, the product simplifies to [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]. This matches one of the given options.
1. Multiply the First Terms:
- Take the [tex]\(-2x\)[/tex] from the first expression and multiply it by the [tex]\(-4x\)[/tex] from the second expression:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Multiply the Outer Terms:
- Take [tex]\(-2x\)[/tex] from the first expression and multiply it by the [tex]\(-3\)[/tex] from the second expression:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Multiply the Inner Terms:
- Take [tex]\(-9y^2\)[/tex] from the first expression and multiply it by the [tex]\(-4x\)[/tex] from the second expression:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Multiply the Last Terms:
- Take [tex]\(-9y^2\)[/tex] from the first expression and multiply it by the [tex]\(-3\)[/tex] from the second expression:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Finally, combine all these results to write the complete polynomial:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Hence, the product simplifies to [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]. This matches one of the given options.
