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Match each expression on the left with its product on the right.

[tex]\[
\begin{array}{ll}
1. & (2d+3)(d^2-1) \\
2. & 2d^3 - d^2 - 5d - 2 \\
3. & (d-2)(2d^2 + 3d + 1) \\
4. & 2d^3 + 2d^2 - 3d - 3 \\
5. & (2d^2 - 3)(d+1) \\
6. & 2d^3 + 3d^2 - 2d - 3 \\
\end{array}
\][/tex]

[tex]\[
\begin{array}{cc}
\text{Expression} & \text{Product} \\
(2d+3)(d^2-1) & 2d^3 + 3d^2 - 2d - 3 \\
(d-2)(2d^2 + 3d + 1) & 2d^3 - d^2 - 5d - 2 \\
(2d^2 - 3)(d+1) & 2d^3 + 2d^2 - 3d - 3 \\
\end{array}
\][/tex]

Now, match each product with its corresponding expression.

Sagot :

GinnyAnswer
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]
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