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Sagot :
Let's match each given expression on the left with its corresponding product on the right one-by-one.
1. Expression 1: [tex]\((2d + 3)(d^2 - 1)\)[/tex]
Matching this expression with the given products:
- [tex]\(2d^3 - d^2 - 5d - 2\)[/tex]
- [tex]\(2d^3 + 2d^2 - 3d - 3\)[/tex]
- [tex]\(2d^3 + 3d^2 - 2d - 3\)[/tex]
Matched Product: [tex]\[2d^3 + 3d^2 - 2d - 3\][/tex]
2. Expression 2: [tex]\(2d^3 - d^2 - 5d - 2\)[/tex]
Matching this product to find its corresponding expression:
- [tex]\((2d + 3)(d^2 - 1)\)[/tex] — already matched
- [tex]\((d - 2)(2d^2 + 3d + 1)\)[/tex]
- [tex]\((2d^2 - 3)(d + 1)\)[/tex]
Matched Expression: [tex]\[(d - 2)(2d^2 + 3d + 1)\][/tex]
3. Expression 3: [tex]\((d - 2)(2d^2 + 3d + 1)\)[/tex]
Matching this expression with the given products:
- [tex]\(2d^3 - d^2 - 5d - 2\)[/tex] — already matched
- [tex]\(2d^3 + 2d^2 - 3d - 3\)[/tex]
- [tex]\(2d^3 + 3d^2 - 2d - 3\)[/tex] — already matched
Matched Product: [tex]\[2d^3 - d^2 - 5d - 2\][/tex]
4. Expression 4: [tex]\(2d^3 + 2d^2 - 3d - 3\)[/tex]
Matching this product to find its corresponding expression:
- [tex]\((2d + 3)(d^2 - 1)\)[/tex] — already matched
- [tex]\((d - 2)(2d^2 + 3d + 1)\)[/tex] — already matched
- [tex]\((2d^2 - 3)(d + 1)\)[/tex]
Matched Expression: [tex]\[(2d^2 - 3)(d + 1)\][/tex]
5. Expression 5: [tex]\((2d^2 - 3)(d + 1)\)[/tex]
Matching this expression with the given products:
- [tex]\(2d^3 - d^2 - 5d - 2\)[/tex] — already matched
- [tex]\(2d^3 + 2d^2 - 3d - 3\)[/tex] — already matched
- [tex]\(2d^3 + 3d^2 - 2d - 3\)[/tex] — already matched
Matched Product: [tex]\[2d^3 + 2d^2 - 3d - 3\][/tex]
6. Expression 6: [tex]\(2d^3 + 3d^2 - 2d - 3\)[/tex]
Matching this product to find its corresponding expression:
- [tex]\((2d + 3)(d^2 - 1)\)[/tex] — already matched
- [tex]\((d - 2)(2d^2 + 3d + 1)\)[/tex] — already matched
- [tex]\((2d^2 - 3)(d + 1)\)[/tex] — already matched
Matched Expression: [tex]\[(2d + 3)(d^2 - 1)\][/tex]
So the final matches are:
1. [tex]\((2d + 3)(d^2 - 1)\)[/tex] matches with [tex]\(2d^3 + 3d^2 - 2d - 3\)[/tex]
2. [tex]\((d - 2)(2d^2 + 3d + 1)\)[/tex] matches with [tex]\(2d^3 - d^2 - 5d - 2\)[/tex]
3. [tex]\((2d^2 - 3)(d + 1)\)[/tex] matches with [tex]\(2d^3 + 2d^2 - 3d - 3\)[/tex]
1. Expression 1: [tex]\((2d + 3)(d^2 - 1)\)[/tex]
Matching this expression with the given products:
- [tex]\(2d^3 - d^2 - 5d - 2\)[/tex]
- [tex]\(2d^3 + 2d^2 - 3d - 3\)[/tex]
- [tex]\(2d^3 + 3d^2 - 2d - 3\)[/tex]
Matched Product: [tex]\[2d^3 + 3d^2 - 2d - 3\][/tex]
2. Expression 2: [tex]\(2d^3 - d^2 - 5d - 2\)[/tex]
Matching this product to find its corresponding expression:
- [tex]\((2d + 3)(d^2 - 1)\)[/tex] — already matched
- [tex]\((d - 2)(2d^2 + 3d + 1)\)[/tex]
- [tex]\((2d^2 - 3)(d + 1)\)[/tex]
Matched Expression: [tex]\[(d - 2)(2d^2 + 3d + 1)\][/tex]
3. Expression 3: [tex]\((d - 2)(2d^2 + 3d + 1)\)[/tex]
Matching this expression with the given products:
- [tex]\(2d^3 - d^2 - 5d - 2\)[/tex] — already matched
- [tex]\(2d^3 + 2d^2 - 3d - 3\)[/tex]
- [tex]\(2d^3 + 3d^2 - 2d - 3\)[/tex] — already matched
Matched Product: [tex]\[2d^3 - d^2 - 5d - 2\][/tex]
4. Expression 4: [tex]\(2d^3 + 2d^2 - 3d - 3\)[/tex]
Matching this product to find its corresponding expression:
- [tex]\((2d + 3)(d^2 - 1)\)[/tex] — already matched
- [tex]\((d - 2)(2d^2 + 3d + 1)\)[/tex] — already matched
- [tex]\((2d^2 - 3)(d + 1)\)[/tex]
Matched Expression: [tex]\[(2d^2 - 3)(d + 1)\][/tex]
5. Expression 5: [tex]\((2d^2 - 3)(d + 1)\)[/tex]
Matching this expression with the given products:
- [tex]\(2d^3 - d^2 - 5d - 2\)[/tex] — already matched
- [tex]\(2d^3 + 2d^2 - 3d - 3\)[/tex] — already matched
- [tex]\(2d^3 + 3d^2 - 2d - 3\)[/tex] — already matched
Matched Product: [tex]\[2d^3 + 2d^2 - 3d - 3\][/tex]
6. Expression 6: [tex]\(2d^3 + 3d^2 - 2d - 3\)[/tex]
Matching this product to find its corresponding expression:
- [tex]\((2d + 3)(d^2 - 1)\)[/tex] — already matched
- [tex]\((d - 2)(2d^2 + 3d + 1)\)[/tex] — already matched
- [tex]\((2d^2 - 3)(d + 1)\)[/tex] — already matched
Matched Expression: [tex]\[(2d + 3)(d^2 - 1)\][/tex]
So the final matches are:
1. [tex]\((2d + 3)(d^2 - 1)\)[/tex] matches with [tex]\(2d^3 + 3d^2 - 2d - 3\)[/tex]
2. [tex]\((d - 2)(2d^2 + 3d + 1)\)[/tex] matches with [tex]\(2d^3 - d^2 - 5d - 2\)[/tex]
3. [tex]\((2d^2 - 3)(d + 1)\)[/tex] matches with [tex]\(2d^3 + 2d^2 - 3d - 3\)[/tex]
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