Answer :
Certainly! Let's solve the problem step by step:
We need to find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
To do this, we'll use the distributive property (also known as the FOIL method for binomials).
1. Distribute [tex]\(-2x\)[/tex] across [tex]\((-4x - 3)\)[/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. Distribute [tex]\(-9y^2\)[/tex] across [tex]\((-4x - 3)\)[/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 the products:
Now add all the results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the final product of the expression is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the choice [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex], which is the correct answer.
We need to find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
To do this, we'll use the distributive property (also known as the FOIL method for binomials).
1. Distribute [tex]\(-2x\)[/tex] across [tex]\((-4x - 3)\)[/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. Distribute [tex]\(-9y^2\)[/tex] across [tex]\((-4x - 3)\)[/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 the products:
Now add all the results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the final product of the expression is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This matches the choice [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex], which is the correct answer.
