Answer :
To find the product of the expression [tex]\((\left(-2 x - 9 y^2\right)(-4 x - 3))\)[/tex], we can use the distributive property (sometimes called the FOIL method for binomials), which involves multiplying each term in the first expression by each term in the second expression. Let's break this down step-by-step.
The given expression is:
[tex]\[
(\left(-2 x - 9 y^2\right)(-4 x - 3))
\][/tex]
We'll distribute each term in [tex]\((-2 x - 9 y^2)\)[/tex] to each term in [tex]\((-4 x - 3)\)[/tex]:
1. First, multiply [tex]\(-2 x\)[/tex] by [tex]\(-4 x\)[/tex]:
[tex]\[
-2 x \cdot -4 x = 8 x^2
\][/tex]
2. Next, multiply [tex]\(-2 x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-2 x \cdot -3 = 6 x
\][/tex]
3. Then, multiply [tex]\(-9 y^2\)[/tex] by [tex]\(-4 x\)[/tex]:
[tex]\[
-9 y^2 \cdot -4 x = 36 x y^2
\][/tex]
4. Finally, multiply [tex]\(-9 y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-9 y^2 \cdot -3 = 27 y^2
\][/tex]
Now, we add up all these products:
[tex]\[
8 x^2 + 6 x + 36 x y^2 + 27 y^2
\][/tex]
So, the final product of the given expression is:
[tex]\[
8 x^2 + 6 x + 36 x y^2 + 27 y^2
\][/tex]
Therefore, the correct answer among the given options is:
[tex]\[
8 x^2 + 6 x + 36 x y^2 + 27 y^2
\][/tex]
The given expression is:
[tex]\[
(\left(-2 x - 9 y^2\right)(-4 x - 3))
\][/tex]
We'll distribute each term in [tex]\((-2 x - 9 y^2)\)[/tex] to each term in [tex]\((-4 x - 3)\)[/tex]:
1. First, multiply [tex]\(-2 x\)[/tex] by [tex]\(-4 x\)[/tex]:
[tex]\[
-2 x \cdot -4 x = 8 x^2
\][/tex]
2. Next, multiply [tex]\(-2 x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-2 x \cdot -3 = 6 x
\][/tex]
3. Then, multiply [tex]\(-9 y^2\)[/tex] by [tex]\(-4 x\)[/tex]:
[tex]\[
-9 y^2 \cdot -4 x = 36 x y^2
\][/tex]
4. Finally, multiply [tex]\(-9 y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
-9 y^2 \cdot -3 = 27 y^2
\][/tex]
Now, we add up all these products:
[tex]\[
8 x^2 + 6 x + 36 x y^2 + 27 y^2
\][/tex]
So, the final product of the given expression is:
[tex]\[
8 x^2 + 6 x + 36 x y^2 + 27 y^2
\][/tex]
Therefore, the correct answer among the given options is:
[tex]\[
8 x^2 + 6 x + 36 x y^2 + 27 y^2
\][/tex]
