Write an expression for the volume of a rectangular prism if the length is 5 feet shorter than some x amount, the width is 3 feet longer than x, and the height is x feet.
x = height
x - 5 = length
x + 3 = width
Volume = length * width * height
I'll let you write the expression.
To find the volume of a rectangular prism, we need to multiply the length, width, and height of the prism.
Let's assign x to the unknown amount.
Given:
Length = x - 5 feet
Width = x + 3 feet
Height = x feet
Now, we can express the volume using these variables:
Volume = Length × Width × Height
Substituting the given values:
Volume = (x - 5) feet × (x + 3) feet × x feet
Simplifying the expression:
Volume = (x^2 - 5x) feet × (x + 3) feet
Expanding the expression:
Volume = (x^3 + 3x^2 - 5x^2 - 15x) feet
Combining like terms:
Volume = (x^3 - 2x^2 - 15x) feet
Therefore, the expression for the volume of the rectangular prism is (x^3 - 2x^2 - 15x) cubic feet.