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Answer :
To find the product [tex]\(( -2x - 9y^2 )(-4x - 3)\)[/tex], we will use the distributive property, which involves distributing each term in the first polynomial by each term in the second polynomial.
Let's break it down step-by-step:
1. Distribute [tex]\(-2x\)[/tex] over [tex]\((-4x - 3)\)[/tex]:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
2. Distribute [tex]\(-9y^2\)[/tex] over [tex]\((-4x - 3)\)[/tex]:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
3. Combine all the results:
- Add all the terms together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This is a polynomial expression resulting from the product of the two given expressions. The like terms have been combined appropriately to yield the final result.
Thus, the product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
Let's break it down step-by-step:
1. Distribute [tex]\(-2x\)[/tex] over [tex]\((-4x - 3)\)[/tex]:
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-2x) \times (-4x) = 8x^2
\][/tex]
- Multiply [tex]\(-2x\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-2x) \times (-3) = 6x
\][/tex]
2. Distribute [tex]\(-9y^2\)[/tex] over [tex]\((-4x - 3)\)[/tex]:
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-4x\)[/tex]:
[tex]\[
(-9y^2) \times (-4x) = 36xy^2
\][/tex]
- Multiply [tex]\(-9y^2\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[
(-9y^2) \times (-3) = 27y^2
\][/tex]
3. Combine all the results:
- Add all the terms together:
[tex]\[
8x^2 + 6x + 36xy^2 + 27y^2
\][/tex]
This is a polynomial expression resulting from the product of the two given expressions. The like terms have been combined appropriately to yield the final result.
Thus, the product is:
[tex]\[ 8x^2 + 6x + 36xy^2 + 27y^2 \][/tex]
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