Answer :
To find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we will use the distributive property. This involves multiplying each term in the first expression by each term in the second expression. Let's go through this step-by-step:
1. Multiply the term [tex]\(-2x\)[/tex] by each term in [tex]\((-4x - 3)\)[/tex]:
- [tex]\(-2x \cdot -4x = 8x^2\)[/tex]
- [tex]\(-2x \cdot -3 = 6x\)[/tex]
2. Multiply the term [tex]\(-9y^2\)[/tex] by each term in [tex]\((-4x - 3)\)[/tex]:
- [tex]\(-9y^2 \cdot -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \cdot -3 = 27y^2\)[/tex]
Now, combine all the resulting terms:
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
This means the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
Thus, the correct answer is:
[tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
1. Multiply the term [tex]\(-2x\)[/tex] by each term in [tex]\((-4x - 3)\)[/tex]:
- [tex]\(-2x \cdot -4x = 8x^2\)[/tex]
- [tex]\(-2x \cdot -3 = 6x\)[/tex]
2. Multiply the term [tex]\(-9y^2\)[/tex] by each term in [tex]\((-4x - 3)\)[/tex]:
- [tex]\(-9y^2 \cdot -4x = 36xy^2\)[/tex]
- [tex]\(-9y^2 \cdot -3 = 27y^2\)[/tex]
Now, combine all the resulting terms:
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
This means the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is:
[tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
Thus, the correct answer is:
[tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
