Distributive Property

Today we looked at how to multiply polynomials. We modelled several questions, and showed how the “groups of” model and the “area model” work together. Example 2(3) is 2 groups of 3, but also a rectangle wth dimensions 2 by 3. We applied that to multiplying polynomials. Here’s 3(x-2) shown in 2 ways.

We practiced several similar examples and noticed that we can multiply the number in front by each term within the brackets. Now we have 2 ways to approach the questions.

When we have (x)(x+1) we run into a problem with the “groups of” method. We don’t know how to represent x groups of something. We need to shift to the area model, or distributive property where we multiply x by each term in the brackets.

We had some breakthroughs with the visual representation, and we talked through how (5)(5) is 5 squared so (x)(x) is x squared. It’ll take some time to solidify the skill, but to practice we did a puzzle in small groups.

I love the puzzles from this site. There are so many neat ones.

we’ll keep working on more algebra next week.