Answer :
To find the product of the two expressions [tex]\((-2x - 9y^2)\)[/tex] and [tex]\((-4x - 3)\)[/tex], we will multiply each term in the first expression by each term in the second expression. We'll then simplify by combining like terms.
Here's a step-by-step breakdown:
1. Distribute [tex]\(-2x\)[/tex]:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
2. Distribute [tex]\(-9y^2\)[/tex]:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
3. Combine all the terms:
- Now, let's bring all these results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The fully expanded and simplified product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 36xy^2 + 6x + 27y^2
\][/tex]
So, the answer to the question is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Here's a step-by-step breakdown:
1. Distribute [tex]\(-2x\)[/tex]:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
2. Distribute [tex]\(-9y^2\)[/tex]:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
3. Combine all the terms:
- Now, let's bring all these results together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
The fully expanded and simplified product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\[
8x^2 + 36xy^2 + 6x + 27y^2
\][/tex]
So, the answer to the question is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
