Question

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

Answer 1

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)

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

Open brackets

$(3d + 2)(d^2 - 1) = 3d \times d^2 - 3d \times 1 + 2 \times d^2 -2 \times 1$

Evaluate the products

$(3d + 2)(d^2 - 1) = 3d^3 - 3d + 2d^2 -2$

Rewrite as:

$(3d + 2)(d^2 - 1) = 3d^3+ 2d^2 - 3d -2$

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

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

Open brackets

$(d - 2)(3d ^2 + 2d + 1) = 3d^3 + 2d^2 + d - 6d^2 - 4d - 2$

Collect like terms

$(d - 2)(3d ^2 + 2d + 1) = 3d^3 + 2d^2 - 6d^2+ d - 4d - 2$

Evaluate the like terms

$(d - 2)(3d ^2 + 2d + 1) = 3d^3 -4d^2 - 3d - 2$

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

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

Open brackets

$(3d^2 - 2)(d + 1) = 3d^3 + 3d^2 -2d - 2$

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

Read more about equivalent expressions at:

brainly.com/question/2972832