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Answer :
To find the product of [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex], we can use the distributive property to expand the expression. Here's a step-by-step solution:
1. Distribute each term in the first parenthesis to each term in the second parenthesis:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex].
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex].
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex].
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex].
2. Calculate each product:
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex]
- [tex]\((-2x) \times (-3) = 6x\)[/tex]
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex]
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex]
3. Combine all the products:
Now, add all these terms together to get the expanded expression:
[tex]\[
8x^2 + 36xy^2 + 6x + 27y^2
\][/tex]
So, the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 36xy^2 + 6x + 27y^2\)[/tex].
1. Distribute each term in the first parenthesis to each term in the second parenthesis:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex].
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex].
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex].
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex].
2. Calculate each product:
- [tex]\((-2x) \times (-4x) = 8x^2\)[/tex]
- [tex]\((-2x) \times (-3) = 6x\)[/tex]
- [tex]\((-9y^2) \times (-4x) = 36xy^2\)[/tex]
- [tex]\((-9y^2) \times (-3) = 27y^2\)[/tex]
3. Combine all the products:
Now, add all these terms together to get the expanded expression:
[tex]\[
8x^2 + 36xy^2 + 6x + 27y^2
\][/tex]
So, the product of the expression [tex]\((-2x - 9y^2)(-4x - 3)\)[/tex] is [tex]\(8x^2 + 36xy^2 + 6x + 27y^2\)[/tex].
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