Answer :
Sure! Let's find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] step-by-step:
1. Distribution Step: We'll distribute each term in the first expression [tex]\((-2x - 9y^2)\)[/tex] by each term in the second expression [tex]\((-4x - 3)\)[/tex].
2. Multiply [tex]\(-2x\)[/tex] by each term:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
3. Multiply [tex]\(-9y^2\)[/tex] by each term:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
4. Combine all the products:
- Add all the terms together: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
The fully expanded expression is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This matches the option: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
1. Distribution Step: We'll distribute each term in the first expression [tex]\((-2x - 9y^2)\)[/tex] by each term in the second expression [tex]\((-4x - 3)\)[/tex].
2. Multiply [tex]\(-2x\)[/tex] by each term:
- [tex]\(-2x \times -4x = 8x^2\)[/tex]
- [tex]\(-2x \times -3 = 6x\)[/tex]
3. Multiply [tex]\(-9y^2\)[/tex] by each term:
- [tex]\(-9y^2 \times -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \times -3 = 27y^2\)[/tex]
4. Combine all the products:
- Add all the terms together: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
The fully expanded expression is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This matches the option: [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex].
