Answer :
To find the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we can use the distributive property, also known as the FOIL method when dealing with binomials, to multiply each term in the first polynomial by each term in the second polynomial.
Follow these steps:
1. Multiply the first terms:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex].
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex].
2. Multiply the outer terms:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex].
- [tex]\((-2x) \times (-3) = 6x\)[/tex].
3. Multiply the inner terms:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex].
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex].
4. Multiply the last terms:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex].
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex].
Finally, combine all these products to get the complete expression:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This is the expanded form of the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
Follow these steps:
1. Multiply the first terms:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex].
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex].
2. Multiply the outer terms:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex].
- [tex]\((-2x) \times (-3) = 6x\)[/tex].
3. Multiply the inner terms:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex].
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex].
4. Multiply the last terms:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex].
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex].
Finally, combine all these products to get the complete expression:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
This is the expanded form of the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
