Answer :
To find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we'll distribute each term from the first binomial with each term from the second binomial. This process is also known as the FOIL method (First, Outer, Inner, Last), but here it involves distributing each term entirely rather than just four terms.
1. First, distribute [tex]\(-2x\)[/tex]:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
2. Next, distribute [tex]\(-9y^2\)[/tex]:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
3. Combine all terms:
By adding all these products together, we get the final expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(\boxed{8x^2 + 6x + 36xy^2 + 27y^2}\)[/tex].
1. First, distribute [tex]\(-2x\)[/tex]:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
2. Next, distribute [tex]\(-9y^2\)[/tex]:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
3. Combine all terms:
By adding all these products together, we get the final expression:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(\boxed{8x^2 + 6x + 36xy^2 + 27y^2}\)[/tex].
