Answer :
Let's solve the problem step by step by expanding the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] using the distributive property, also known as the FOIL method (First, Outer, Inner, Last):
1. First: Multiply the first terms of each binomial.
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Outer: Multiply the outer terms.
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Inner: Multiply the inner terms.
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Last: Multiply the last terms of each binomial.
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Next, add all these results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the expanded expression is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]. This matches the third option in the list provided.
1. First: Multiply the first terms of each binomial.
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Outer: Multiply the outer terms.
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Inner: Multiply the inner terms.
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Last: Multiply the last terms of each binomial.
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Next, add all these results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the expanded expression is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]. This matches the third option in the list provided.
