Answer :
Sure! Let's solve the problem step-by-step using the distributive property.
Given the expression to expand:
[tex]\[
(-2x - 9y^2)(-4x - 3)
\][/tex]
To expand this, we apply the distributive property by multiplying each term in the first parentheses by each term in the second parentheses.
1. Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
2. Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
3. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
4. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
Now, combine all these results to find the product:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the expanded expression is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So the correct answer is option c:
[tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
Given the expression to expand:
[tex]\[
(-2x - 9y^2)(-4x - 3)
\][/tex]
To expand this, we apply the distributive property by multiplying each term in the first parentheses by each term in the second parentheses.
1. Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
2. Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
3. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
4. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
Now, combine all these results to find the product:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the expanded expression is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So the correct answer is option c:
[tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
