Answer :
Let's solve the problem step-by-step by expanding the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
First, we'll use the distributive property to expand this expression. The distributive property tells us to multiply each term in the first parenthesis by each term in the second parenthesis:
1. Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, add up all these terms to find the product:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Let's check which option matches this result:
- The correct expression is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Therefore, the correct answer is:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
First, we'll use the distributive property to expand this expression. The distributive property tells us to multiply each term in the first parenthesis by each term in the second parenthesis:
1. Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
2. Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
3. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
4. Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
Now, add up all these terms to find the product:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Let's check which option matches this result:
- The correct expression is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
Therefore, the correct answer is:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
