Answer :
Sure! Let's solve the problem step by step.
We are asked to find the product of [tex]\(\left(-2x - 9y^2\right)(-4x - 3)\)[/tex].
1. Distribute each term in the first polynomial to each term in the second polynomial:
[tex]\[
(-2x - 9y^2)(-4x - 3) = (-2x) \cdot (-4x) + (-2x) \cdot (-3) + (-9y^2) \cdot (-4x) + (-9y^2) \cdot (-3)
\][/tex]
2. Multiply each pair of terms:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
3. Combine all these terms:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product [tex]\(\left(-2x - 9y^2\right)(-4x - 3)\)[/tex] simplifies to:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
From the given choices, the correct answer is:
[tex]\[ \boxed{8x^2 + 6x + 36x y^2 + 27y^2} \][/tex]
We are asked to find the product of [tex]\(\left(-2x - 9y^2\right)(-4x - 3)\)[/tex].
1. Distribute each term in the first polynomial to each term in the second polynomial:
[tex]\[
(-2x - 9y^2)(-4x - 3) = (-2x) \cdot (-4x) + (-2x) \cdot (-3) + (-9y^2) \cdot (-4x) + (-9y^2) \cdot (-3)
\][/tex]
2. Multiply each pair of terms:
[tex]\[
(-2x) \cdot (-4x) = 8x^2
\][/tex]
[tex]\[
(-2x) \cdot (-3) = 6x
\][/tex]
[tex]\[
(-9y^2) \cdot (-4x) = 36xy^2
\][/tex]
[tex]\[
(-9y^2) \cdot (-3) = 27y^2
\][/tex]
3. Combine all these terms:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
So, the product [tex]\(\left(-2x - 9y^2\right)(-4x - 3)\)[/tex] simplifies to:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
From the given choices, the correct answer is:
[tex]\[ \boxed{8x^2 + 6x + 36x y^2 + 27y^2} \][/tex]
