Answer :
Sure, let's find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] step by step using the distributive property:
1. First, distribute [tex]\((-2x)\)[/tex]:
- Multiply [tex]\((-2x)\)[/tex] by [tex]\((-4x)\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Multiply [tex]\((-2x)\)[/tex] by [tex]\((-3)\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
2. Next, distribute [tex]\((-9y^2)\)[/tex]:
- Multiply [tex]\((-9y^2)\)[/tex] by [tex]\((-4x)\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\((-9y^2)\)[/tex] by [tex]\((-3)\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
3. Combine all the terms:
- The first product is [tex]\(8x^2\)[/tex]
- The second product is [tex]\(6x\)[/tex]
- The third product is [tex]\(36xy^2\)[/tex]
- The fourth product is [tex]\(27y^2\)[/tex]
4. Write the final expression by combining all these terms:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
The correct option from the list provided is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
1. First, distribute [tex]\((-2x)\)[/tex]:
- Multiply [tex]\((-2x)\)[/tex] by [tex]\((-4x)\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Multiply [tex]\((-2x)\)[/tex] by [tex]\((-3)\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
2. Next, distribute [tex]\((-9y^2)\)[/tex]:
- Multiply [tex]\((-9y^2)\)[/tex] by [tex]\((-4x)\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\((-9y^2)\)[/tex] by [tex]\((-3)\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
3. Combine all the terms:
- The first product is [tex]\(8x^2\)[/tex]
- The second product is [tex]\(6x\)[/tex]
- The third product is [tex]\(36xy^2\)[/tex]
- The fourth product is [tex]\(27y^2\)[/tex]
4. Write the final expression by combining all these terms:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
Therefore, the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
The correct option from the list provided is:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
