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Match each expression on the left with its product on the right. (3d + 2)(d ^ 2 - 1); 3d ^ 3 + 2d ^ 2 - 3d - 2; (d - 2)(3d ^ 2 + 2d + 1); 3d ^ 3 + 3d ^ 2 - 2d - 2; (3d ^ 2 - 2)(d + 1); 3d ^ 3 - 4d ^ 2 - 3d - 2

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MrRoyal

The expressions and their products are:

  • (3d + 2)(d^2 - 1) and 3d^3+ 2d^2 - 3d  -2
  • (d - 2)(3d ^2 + 2d + 1) and 3d^3 -4d^2  - 3d - 2
  • (3d^2 - 2)(d + 1) and 3d^3 + 3d^2 -2d - 2

The expressions are given as:

  • (3d + 2)(d ^2 - 1)
  • (d - 2)(3d ^2 + 2d + 1)
  • (3d^2 - 2)(d + 1)

Expanding the expression (3d + 2)(d^2 - 1)

[tex](3d + 2)(d^2 - 1)[/tex]

Open brackets

[tex](3d + 2)(d^2 - 1) = 3d \times d^2 - 3d \times 1 + 2 \times d^2 -2 \times 1[/tex]

Evaluate the products

[tex](3d + 2)(d^2 - 1) = 3d^3 - 3d + 2d^2 -2[/tex]

Rewrite as:

[tex](3d + 2)(d^2 - 1) = 3d^3+ 2d^2 - 3d -2[/tex]

Expanding the expression (d - 2)(3d ^2 + 2d + 1)

[tex](d - 2)(3d ^2 + 2d + 1)[/tex]

Open brackets

[tex](d - 2)(3d ^2 + 2d + 1) = 3d^3 + 2d^2 + d - 6d^2 - 4d - 2[/tex]

Collect like terms

[tex](d - 2)(3d ^2 + 2d + 1) = 3d^3 + 2d^2 - 6d^2+ d - 4d - 2[/tex]

Evaluate the like terms

[tex](d - 2)(3d ^2 + 2d + 1) = 3d^3 -4d^2 - 3d - 2[/tex]

Expanding the expression (3d^2 - 2)(d + 1)

[tex](3d^2 - 2)(d + 1)[/tex]

Open brackets

[tex](3d^2 - 2)(d + 1) = 3d^3 + 3d^2 -2d - 2[/tex]

Hence, the equivalent expression of (3d^2 - 2)(d + 1) is 3d^3 + 3d^2 -2d - 2

Read more about equivalent expressions at:

https://brainly.com/question/2972832

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