a cube has a side length of 4x-3, express its volume as a polynomial
s = 4x - 3
V = s^3
V = (4x - 3)^3
V = (4x - 3)^2 (4x - 3)
I leave the multiplication to you.
To express the volume of a cube with a side length of 4x-3 as a polynomial, we need to use the formula for the volume of a cube.
The formula for the volume of a cube is V = s^3, where V represents the volume and s represents the side length.
In this case, the side length of the cube is 4x-3, so we can substitute this value into the formula:
V = (4x-3)^3
To find the volume, we need to simplify the expression (4x-3)^3.
To simplify, we can cube each term inside the parentheses using the formula (a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3.
In this case, a = 4x and b = 3:
V = (4x)^3 - 3(4x)^2(3) + 3(4x)(3^2) - (3)^3
Simplifying further:
V = 64x^3 - 3(16x^2)(3) + 3(4x)(9) - 27
V = 64x^3 - 144x^2 + 108x - 27
Therefore, the volume of the cube with a side length of 4x-3 can be expressed as the polynomial 64x^3 - 144x^2 + 108x - 27.