Answer :
To find the product of [tex]\(( -2x - 9y^2 )( -4x - 3 )\)[/tex], we'll use the distributive property. Let's break it down step-by-step:
1. Distribute [tex]\(-2x\)[/tex] across [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. Distribute [tex]\(-9y^2\)[/tex] across [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 terms:
Combining the results from all the distributions, we get:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This expression matches the third option listed in the question:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
So, the product of [tex]\(( -2x - 9y^2 )( -4x - 3 )\)[/tex] is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
1. Distribute [tex]\(-2x\)[/tex] across [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. Distribute [tex]\(-9y^2\)[/tex] across [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 terms:
Combining the results from all the distributions, we get:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This expression matches the third option listed in the question:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
So, the product of [tex]\(( -2x - 9y^2 )( -4x - 3 )\)[/tex] is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
