Answer :
To find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we need to use the distributive property, also known as the FOIL method when dealing with binomials. Let's expand the expression step-by-step:
1. First Terms: Multiply the first terms of each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Outer Terms: Multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Inner Terms: Multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Last Terms: Multiply the last terms:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, combine all these results to get the expanded expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This expanded expression matches one of the given options:
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
So, the correct product is:
[tex]\[ \boxed{8x^2 + 6x + 36xy^2 + 27y^2} \][/tex]
1. First Terms: Multiply the first terms of each binomial:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Outer Terms: Multiply the outer terms:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Inner Terms: Multiply the inner terms:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Last Terms: Multiply the last terms:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, combine all these results to get the expanded expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This expanded expression matches one of the given options:
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
So, the correct product is:
[tex]\[ \boxed{8x^2 + 6x + 36xy^2 + 27y^2} \][/tex]
