2D, 3D Cubic
Multiplication can be represented with sides and space.
What are the dimension of the gold section?
If x is measured meters, what will the area of the gold square be measured in?
When 2 lengths are multiplied, we get a square made up of four boxes shown above in two dimensions. If we multiply by three lengths, what shape will the result be? How many sections will we have?
When you are ready, scroll down to see.
Note the similarities between these objects in 2 and 3 dimensions. Rotate the cube on the right to examine it from all angles and answer the questions below
Of the 8 sections of the cube, if the shapes are the same color, they are the same size. How many of each type are there?
If the Large Yellow-Orange cube has length x, and the small lime green cube has length a, what are the dimensions of the blue prism? What about the pink prism?
Using the lengths of the cube as (x+a), what would the expanded form of [math]\left(x+a\right)^3[/math] be?
Bonus Question (Optional)
given a cubic of form[br][math]x^3+cx+d[/math], [br]make a generalized solution for x.