Answer :
Let's find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] step-by-step:
1. Distribute the first term, [tex]\(-2x\)[/tex], across [tex]\((-4x - 3)\)[/tex]:
- Multiply: [tex]\(-2x \times -4x = 8x^2\)[/tex]
- Multiply: [tex]\(-2x \times -3 = 6x\)[/tex]
2. Distribute the second term, [tex]\(-9y^2\)[/tex], across [tex]\((-4x - 3)\)[/tex]:
- Multiply: [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- Multiply: [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
3. Combine all the results:
- From the first distribution, we have: [tex]\(8x^2 + 6x\)[/tex]
- From the second distribution, we have: [tex]\(36xy^2 + 27y^2\)[/tex]
Putting all these terms together, the complete product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This corresponds to the choice:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
So the correct answer is the option: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
1. Distribute the first term, [tex]\(-2x\)[/tex], across [tex]\((-4x - 3)\)[/tex]:
- Multiply: [tex]\(-2x \times -4x = 8x^2\)[/tex]
- Multiply: [tex]\(-2x \times -3 = 6x\)[/tex]
2. Distribute the second term, [tex]\(-9y^2\)[/tex], across [tex]\((-4x - 3)\)[/tex]:
- Multiply: [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- Multiply: [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
3. Combine all the results:
- From the first distribution, we have: [tex]\(8x^2 + 6x\)[/tex]
- From the second distribution, we have: [tex]\(36xy^2 + 27y^2\)[/tex]
Putting all these terms together, the complete product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This corresponds to the choice:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
So the correct answer is the option: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
