Question

The volume of a rectangular prism is 2x^3 - 6x^2 + 8x , and the volume of a cube is 27x^3. What is the total volume of the prism and the cube?

Answer 1

`\displaystyle V_(P + C) = 29x^3 - 6x^2 + 8x`

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

Terms/Coefficients

Explanation:

Step 1: Define

Identify.

`\displaystyle V_P = 2x^3 - 6x^2 + 8x`

`\displaystyle V_C = 27x^3`

Step 2: Find Combined Volume

1. [Set up] Add:
   `\displaystyle V_P + V_C = V_(P + C)`
2. Substitute in variables:
   `\displaystyle V_(P + C) = 27x^3 + 2x^3 - 6x^2 + 8x`
3. Combine like terms:
   `\displaystyle V_(P + C) = 29x^3 - 6x^2 + 8x`