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schepotkina [342]
3 years ago
6

Which group of expressions could represent the dimensions of a rectangular prism with a volume of 2y3 + 15y2 + 28y?

Mathematics
1 answer:
Vitek1552 [10]3 years ago
3 0

Answer:

C. y, y + 2, 2y + 14

Step-by-step explanation:

Given

Volume = 2y^3 + 15y^2 + 28y

Required

Determine which set of dimensions is applicable

The volume of a rectangular prism is calculated as:

Volume = Length * Width * Height

So, to solve this question, we have to test each options using the above formula

A. y, y + 4 and 2y + 7

Volume = y * (y + 4) * (2y + 7)

Open brackets

Volume = y * (y * 2y+ 4* 2y + y * y+ 4* 7)

Volume = y(2y^2+ 8y + y^2+ 28)

Volume = 2y^3+ 8y^2 + y^3+ 28y

Collect Like Terms

Volume = 2y^3 + y^3+ 8y^2+ 28y

Volume = 3y^3+ 8y^2+ 28y

B. y, y + 7, 2y + 4

Volume = y * (y + 7) * (2y + 4)

Open brackets

Volume = y * (y * (2y + 4)+ 7* (2y + 4))

Volume = y * (2y^2 + 4y+ 14y + 28)

Volume = y * (2y^2 + 18y+ 28)

Volume = 2y^3 + 18y^2+ 28y

C. y, y + 2, 2y + 14

Volume = y * (y + 2) * (2y + 14)

Open brackets

Volume = y * (y* (2y + 14) + 2* (2y + 14))

Volume = y * (2y^2 + 14y + 4y + 28)

Volume = y * (2y^2 + 18y + 28)

Volume = 2y^3 + 18y^2 + 28y

<em>There's no need to check the last option because option c answers the question.</em>

<em>Hence, the dimension is y, y + 2, 2y + 14 </em>

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