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(Video) Multiplying Polynomials

by mathman1024

Here's a video by mathman1024 that shows you how to multiply two polynomials together. He goes over two different methods: distributing and box method.

To multiply using the box method you make a box where each cell row and column is a term. Using the example $(2x+7)(3x-5)$ we would set ours up like so:

It doesn't matter which polynomial goes on top and which goes on the side. Next, for each cell, multiply the the term for the row by the term for the column. So our first box will be $3x\cdot2x$ and so on.

Finally, we combine the terms and simplify. $$\begin{gather}6x^2+21x-10x-35\\ =6x^2+11x-35\end{gather}$$

(Video) FOIL to Multiply

by mathman1024

This video by mathman1024 covers binomial multiplication through a few different methods, including multiplication with tables.

Note: it doesn't matter which you put on top or on the side.

After you solved for each cell you notice that the like terms are on the diagonals.

Finally, you just add the like terms together and then construct your polynomial. $$2x^3-3x^2-35x+36$$

Multiply Binomials: Using Tables

There are two main ways to multiply binomails: FOIL and using tables.

In this lesson, we'll look at using the table method.

Multiplying Binomials: Tables

So far, we've seen a couple of different ways that we can multiply binomials. In this lesson, we'll cover how to multiply binomials using tables.

It's easiest to learn by walking through an example!

Let's say we are trying multiply:

$$(2x+1)(3x+2)$$

Step 1: Draw the box and align the values

Your first step is to draw the box and assign the individual terms to the spaces around the box.

Make sure you watch your negative signs, if you have any!

Step 2: Multiply the terms in the boxes

Sometimes, it'll be helpful to write out the multiplication in the boxes.

Step 3: Multiply through

Step 4: Convert from the tables to an expression

Your last step is to remove the terms from the table and into a mathematical expression.

$$6x^2 + 3x + 4x + 2$$

Combine like terms!

$$6x^2 + 7x + 2$$