Answer :
To find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we will use the distributive property, which involves multiplying each term in the first parentheses by each term in the second parentheses. Let's break it down step-by-step:
1. Distribute [tex]\(-2x\)[/tex] to both terms in the second parentheses:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
2. Distribute [tex]\(-9y^2\)[/tex] to both terms in the second parentheses:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
3. Combine all the results:
- From step 1, we have [tex]\(8x^2\)[/tex] and [tex]\(6x\)[/tex].
- From step 2, we have [tex]\(36xy^2\)[/tex] and [tex]\(27y^2\)[/tex].
So, when you put them all together, you get the product:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This matches the option: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
1. Distribute [tex]\(-2x\)[/tex] to both terms in the second parentheses:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
2. Distribute [tex]\(-9y^2\)[/tex] to both terms in the second parentheses:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
3. Combine all the results:
- From step 1, we have [tex]\(8x^2\)[/tex] and [tex]\(6x\)[/tex].
- From step 2, we have [tex]\(36xy^2\)[/tex] and [tex]\(27y^2\)[/tex].
So, when you put them all together, you get the product:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This matches the option: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
