This week in math 10 we focused on multiplying binomials, polynomials and how to use models to solve equations. I believe that the most important concept I learned this week was how to use models such as algebra tiles and area models to solve binomials and polynomials problems. I think that this is the most important concept I learned this week because sometimes it can be difficult to always solve equations using algebra and a great alternative is to solve them by seeing them visually. A new trick I learned this week was when I am stuck on an equation it can be helpful to try and use other approaches to solve it.

 

Algebra Tiles:

Algebra tiles are a great choice to visually solve binomial equations, but they are not always useful because algebra tiles can only solve simple equations.

The first step is to draw the terms in the left bracket and put them above the top horizontal line;

Then draw the terms from the right bracket and put them beside the left vertical line;

Then combine the terms that are on the horizontal line with the terms on the left vertical line by multiplying them together;

The last step is to either color in the boxes and rectangles if they are positive or leave them blank if they are negative. Once that is done you can determine your final answer.

 

Area Modelling:

Area Modelling is an even better tool to use when solving almost all polynomial equations because no matter how complicated the equation is, area modelling will still work.

When using area modelling the first step is to separate the different terms in the left bracket and place them at the top of the rectangle;

Then separate the terms in the right bracket and place them on the left side of the rectangle;

Once all the terms have been separated multiply each term with one another until each box has been filled;

Then the last step is to add and simplify all the terms together to get the final answer.