Math Blog Week 8

This week in math we learned about polynomials.

We learned three methods for multiplying a polynomial by a polynomial.

The first method we learned was using algebra tiles to create diagrams, first draw two lines that form a one cornered graph shape and draw tiles that match the question along the top and side, an tile or variables are represented by a 1x rectangle, an tile is represented by an x square, and a 1 tile is represented by a 1×1 tile, then in the empty space you draw tiles that are proportioned to the existing ones. If our equation is (x-3)(-x+5) then our graph will look like this:

It’s important to remember about the rules of multiplying negatives here. The 4 drawbacks of this method however are: It becomes incredibly complex to use at larger numbers, it’s useless with more than 2 polynomials, and you can’t accurately portray any exponent higher than 2 as the product, or exponents in the polynomials.

The second method is called an area diagram and slightly more complex but is easier to do with larger numbers or higher polynomials, we use a graph like the previous one however we don’t make any algebra tiles instead we insert the individual parts of the equation along the sides and multiply them by each other and add the answers together. This one can be used for much more than just polynomials, for example we could calculate 24×23 without a calculator. Take the question . If we wanted to create this graph it would look something like this:

The main drawback of this is that it gets complicated with larger polynomials but it’s still my personal favourite for it’s sheer practicality for multiplication.

The last one is perhaps the most complicated of the 3 techniques simply because it involves the distributive property. Take for example, first we take x from the first part and multiply the entire second part by it giving us , now we do the same thing with the other one giving us , now we just add them together giving us the final answer of . Simple huh? Try it with more and larger polynomials.