There are three ways to visualize of polynomials in order to get to your answer.

The first one is using the area model, such as the product of (+8)(+8) would be expanded to it’s answer of -64. You might wonder why we would use this representation, but it’s to know that the product of two binomials is the same thing as having four monomial products when solving on your diagram. This is an excellent way to, help you face with big numbers of polynomials.

• This is an easy way to solve your long multiplication with this model by spitting them up into ten. For example, 32×34 would be 30 and 2 with the other pair of 30 and 4. Which is a way to show they can separate into four products.
• What is “like terms”? Great question! It is when the variable of two or more would have the same degree that are “like” to each other. And always remember to add them up to get to your final answer.

 

There is a second representation, which is using algebra tiles to draw out each number by its variable that is indicated of how much of tiles you need to draw with the coefficient.  In every situation, we know that the shaded tile are meant to be positive. And the titles that are not shaded is the negative that we must change in some problems. When the negative title hits the positive, then the multiplication rule says it would become a negative title.

We can use their representation to demonstrate that we can multiply the monomial by a polynomial in the expression. It’s time to take a note that the first bracket would be located at the top of the chart. While the second bracket would come in to the left side for us to draw out the shapes. Then that would give us an understanding what our variables would be when we draw the lines that are attached to each other.

 

Here we have been distributive property, we can indicate to draw out the arrows to point that the number is being multiplied to each terms in the bracket. Their formula is to use the following, if (b+c) is equal to ab +ac. And the exponent rule with by is equal to (+laxtex b^$), which had expanded and simplified our polynomial expression.

And a quick note that when a 2a is being multiplied by 5c, it is meant to be the 10ac when using the alphabetical order. Which leads to become harder with letters that are p,q,x,y,z that would often appear in the expression when solving in your work.