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# Multiplying monomials by polynomials: area model

CCSS.Math:

## Video transcript

we're asked to express the area of the entire rectangle below as a trinomial we have our rectangle here and it's broken up into these three smaller rectangles and we see for all of these rectangles the height here is 4 units and then the widths are expressed in terms or at least the first two are expressed in terms of X and then this last one has a width of 2 so what's the area of the entire rectangle encourage you to pause the video and think about it most the area of this blue this blue it looks like a square but it will just call it a rectangle which all squares are rectangles so that's safe well it's going to be the height times the width so the area here is going to be the height which is 4 times the width which is x squared and then we do that we want to add the area of this of this I guess we could say this salmon colored rectangle and well that's going to be the height 4 times the width 3 X so we could say 4 times 3 X we could write it like that but what is 4 times 3 X well it's going to be 12 X I have 3 X 4 times I have 12 X's so that's going to be 12 X 12 X is the area of this salmon colored rectangle and then finally the area of this green rectangle we actually can figure out it exactly we don't even have to express it in terms of a variable its height is 4 its width is 2 so the area is going to be 4 times 2 or 8 and we are done