Answer :
To find the product [tex]\(\left(-2x - 9y^2\right)(-4x - 3)\)[/tex], we'll use the distributive property to multiply each term in the first parenthesis by each term in the second parenthesis.
1. Multiply the first terms:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Multiply the first term by the second term:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Multiply the second term by the first term:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Multiply the second terms:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, we will combine all the resulting terms:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This is the expanded form of the product, which matches the expression [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]. So, the correct choice from the options is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
1. Multiply the first terms:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Multiply the first term by the second term:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Multiply the second term by the first term:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Multiply the second terms:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, we will combine all the resulting terms:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This is the expanded form of the product, which matches the expression [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]. So, the correct choice from the options is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
