how do i Write an expanded expression for the volume of the cube with a side length of 3x+2 cm.
volume = (3x+2)^3
= (3x+2)(3x+2)(3x+2)
expand and simplify
To write an expanded expression for the volume of a cube with a side length of (3x + 2) cm, you need to understand the formula for the volume of a cube. The volume of a cube is given by the formula:
Volume = (side length)^3
Therefore, to find the volume of a cube with a side length of (3x + 2) cm, you can substitute (3x + 2) for the side length in the formula:
Volume = [(3x + 2)]^3
Now, let's expand the expression using the binomial expansion. For a cube, you need to multiply the side length by itself three times (cube it). To expand this expression, you can use the binomial expansion, which is based on the binomial theorem:
(3x + 2)^3 = (3x + 2)(3x + 2)(3x + 2)
To expand this, you distribute each term to every term in the second and third parentheses:
(3x + 2)(3x + 2)(3x + 2) = (3x * 3x * 3x) + (3x * 3x * 2) + (3x * 2 * 3x) + (3x * 2 * 2) + (2 * 3x * 3x) + (2 * 3x * 2) + (2 * 2 * 3x) + (2 * 2 * 2)
Simplifying this expression gives you:
27x^3 + 36x^2 + 12x + 8
Therefore, the expanded expression for the volume of a cube with a side length of (3x + 2) cm is:
Volume = 27x^3 + 36x^2 + 12x + 8 cubic cm