The dimensions or a fish tank ( rectangular prism ) are x, 3x+2, and 2x-4. Express the volume of the fish tank as a simplified polynomial.
v = x(3x+2)(2x-4)
Now just expand that out
To find the volume of a rectangular prism, you need to multiply its length, width, and height. In this case, the given dimensions of the fish tank are x, 3x+2, and 2x-4.
So, the volume (V) of the fish tank can be expressed as V = (length) x (width) x (height).
Substitute the given dimensions into the equation:
V = x * (3x+2) * (2x-4)
To simplify the polynomial expression, you can start by multiplying the terms:
V = x * (6x^2 - 8x + 4x - 8)
Next, simplify the expression further by combining like terms within the parentheses:
V = x * (6x^2 - 4x - 8)
Finally, distribute the x across the terms inside the parentheses:
V = 6x^3 - 4x^2 - 8x
So, the volume of the fish tank can be expressed as the simplified polynomial 6x^3 - 4x^2 - 8x.