Question

Which group of expressions could represent the dimensions of a rectangular prism with a volume of 2y3 + 15y2 + 28y?
A. y, y + 4, 2y + 7
B. y, y + 7, 2y + 4
C. y, y + 2, 2y + 14
D. y, y + 14, 2y + 2

Answer 1

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

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

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

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

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

There's no need to check the last option because option c answers the question.

Hence, the dimension is y, y + 2, 2y + 14