Answer :
Sure! Let's solve the problem step by step.
We need to find the product of the following expression:
[tex]\[
(-2x - 9y^2)(-4x - 3)
\][/tex]
We'll do this by distributing each term in the first binomial over each term in the second binomial.
1. Distribute [tex]\(-2x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
2. Distribute [tex]\(-9y^2\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
3. Combine all the terms:
The resulting expression after distribution and simplifying is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Looking at the options provided:
- [tex]\(-8x^2 - 6x - 36xy^2 - 27y^2\)[/tex]
- [tex]\(-14x^2 - 36xy^2 + 27y^2\)[/tex]
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
- [tex]\(14x^2 + 36xy^2 + 27y^2\)[/tex]
The correct product based on our calculations is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the correct choice is:
[tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
We need to find the product of the following expression:
[tex]\[
(-2x - 9y^2)(-4x - 3)
\][/tex]
We'll do this by distributing each term in the first binomial over each term in the second binomial.
1. Distribute [tex]\(-2x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
2. Distribute [tex]\(-9y^2\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
3. Combine all the terms:
The resulting expression after distribution and simplifying is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Looking at the options provided:
- [tex]\(-8x^2 - 6x - 36xy^2 - 27y^2\)[/tex]
- [tex]\(-14x^2 - 36xy^2 + 27y^2\)[/tex]
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
- [tex]\(14x^2 + 36xy^2 + 27y^2\)[/tex]
The correct product based on our calculations is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the correct choice is:
[tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
