Algebra tiles 

Today we are looking at representing this kind of expression with algebra tiles.

We can show it as two groups of 3x+1 

Which is the same thing as 6x+2

But we can also see each expression (the 2 and the 3x+1) as dimensions of a rectangle.

The product of these two dimensions would be the area of the rectangle.  We fill in a rectangle with length of 3x+1 and width of 2 and we get 6x+2 as an answer. 

The area model is particularly useful when multiplying expressions with variables in both length and width.

X(2X+1)=2X^2+X