Let's write the area of the rectangle as a product first. Then we will write it as a sum.
As a Product
To write the area as a product, let's remind ourselves of how we find the area of a rectangle.
A= l w
Let's identify the length and the width of our rectangle.
From the diagram, we see that the rectangle has a length of two x-tiles and four 1-tiles. The width is made up of one x-tile and two 1-tiles. Now we can express the area as a product of these sums.
A=(2x+4)(x+2)
As a Sum
To write the area as a sum, we have to add the different tiles. We have two x^2-tiles, eight x-tiles and eight 1-tiles.
A=2x^2+8x+8
Conclusion
Since we found two expressions for the area of this rectangle, we can conclude that
(2x+4)(x+2)=2x^2+8x+8
