This week in math I learned how to use are models to multiply double digit numbers by each other and binomials too.

In this case where we only have double digit numbers to multiply by, we draw a 2×2 grid, one box for each digit in the number, then split the number into it’s tens and ones and put it along one of the axis. Now, for each one of these grid spaces you multiply the numbers that fall under that grid space, after doing this for every grid space, add all of your answers and that is your product as we see in the diagram, 1200 + 160 + 30 + 4 = 1394 which is the answer to 34 x 41.

 

Using an area model to multiply polynomials works very similarly to just multiplying numbers together, each term in the polynomial gets its own row/column and for each grid space you multiply the numbers that fall under that grid space, making sure to abide by exponent multiplication law with the variables, putting like terms together and putting everything in descending order. As you can see in this diagram, 2x and 4x multiplying together gets you because of exponent multiplication law and 12x and -8x are like terms that get put together giving you 4x. Do everything correctly and put everything in the right order and that’s your answer.