Answer :
To find the product [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], let's break it down step by step:
1. Distribute each term:
- First, take [tex]\(-2x\)[/tex] and distribute it to both terms inside the second parenthesis:
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex]
- [tex]\((-2x) \times (-3) = 6x\)[/tex]
2. Distribute each term continued:
- Now, take [tex]\(-9y^2\)[/tex] and distribute it to both terms inside the second parenthesis:
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex]
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex]
3. Combine all the products:
- The results from the distributions give us:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This final expression [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex] is the expanded form of the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
1. Distribute each term:
- First, take [tex]\(-2x\)[/tex] and distribute it to both terms inside the second parenthesis:
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex]
- [tex]\((-2x) \times (-3) = 6x\)[/tex]
2. Distribute each term continued:
- Now, take [tex]\(-9y^2\)[/tex] and distribute it to both terms inside the second parenthesis:
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex]
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex]
3. Combine all the products:
- The results from the distributions give us:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This final expression [tex]\(8x^2 + 6x + 36xy^2 + 27y^2\)[/tex] is the expanded form of the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex].
