Answer :
To find the product [tex]\((\left(-2x - 9y^2\right)(-4x - 3)\)[/tex], we need to apply the distributive property, also known as the FOIL method (First, Outer, Inner, Last) for binomials.
Let's break it down step by step:
1. First Terms:
- Multiply the first terms of each binomial: [tex]\((-2x) \times (-4x)\)[/tex]
- This equals [tex]\(8x^2\)[/tex].
2. Outer Terms:
- Multiply the outer terms: [tex]\((-2x) \times (-3)\)[/tex]
- This equals [tex]\(6x\)[/tex].
3. Inner Terms:
- Multiply the inner terms: [tex]\((-9y^2) \times (-4x)\)[/tex]
- This equals [tex]\(36xy^2\)[/tex].
4. Last Terms:
- Multiply the last terms of each binomial: [tex]\((-9y^2) \times (-3)\)[/tex]
- This equals [tex]\(27y^2\)[/tex].
Now, combine all these terms together:
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
This is the fully expanded and simplified expression for the given question. Therefore, the correct product is:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
Let's break it down step by step:
1. First Terms:
- Multiply the first terms of each binomial: [tex]\((-2x) \times (-4x)\)[/tex]
- This equals [tex]\(8x^2\)[/tex].
2. Outer Terms:
- Multiply the outer terms: [tex]\((-2x) \times (-3)\)[/tex]
- This equals [tex]\(6x\)[/tex].
3. Inner Terms:
- Multiply the inner terms: [tex]\((-9y^2) \times (-4x)\)[/tex]
- This equals [tex]\(36xy^2\)[/tex].
4. Last Terms:
- Multiply the last terms of each binomial: [tex]\((-9y^2) \times (-3)\)[/tex]
- This equals [tex]\(27y^2\)[/tex].
Now, combine all these terms together:
- [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex]
This is the fully expanded and simplified expression for the given question. Therefore, the correct product is:
[tex]\[8x^2 + 6x + 36xy^2 + 27y^2\][/tex]
