Answer :
To solve the problem of finding the product [tex]\(( -2x - 9y^2)(-4x - 3)\)[/tex], we need to distribute each term in the first polynomial by each term in the second polynomial. Here's a step-by-step explanation:
1. First, distribute [tex]\(-2x\)[/tex] over each term in the second parenthesis [tex]\((-4x - 3)\)[/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] over each term in the second parenthesis [tex]\((-4x - 3)\)[/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 results from the distributions:
The expression becomes:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This is the expanded polynomial after multiplying the two given polynomials. Therefore, the correct product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This matches the option: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
1. First, distribute [tex]\(-2x\)[/tex] over each term in the second parenthesis [tex]\((-4x - 3)\)[/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] over each term in the second parenthesis [tex]\((-4x - 3)\)[/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 results from the distributions:
The expression becomes:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This is the expanded polynomial after multiplying the two given polynomials. Therefore, the correct product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This matches the option: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].