Wait, does it really matter which order you put it in? For example, for the practice question I instead did x squared plus 15 -8x? or should I put it like x squared -8x plus 15? And if I do get it right, which is the most recommended?

It does matter because the exponents the x^2 is larger than x and x is larger than the plain number

Why can't we just use the foil method instead. (First Outer, Inner, and Last

It is better to know all the methods so that you can expand what you can do. FOIL works great for (x+2)(x-4) but what if later on in math you have to multiply (x^2 + 2x - 3)(x + 5)? FOIL will not get you very far, but box method or distribution method will.

Isn't this just the FOIL method? First, Outside, Inside, and Last. That mnemonic helped immensely with my understanding of multiplying polynomials.

This is similar to FOIL, but it is called the double distribution method, you distribute one of the binomials to all the parts of the other binomial. It is important to learn beyond FOIL because it is not limited to just binomials. You could do (x^2+2x+5)(x-4) using the distribution method. x(x^2+2x+5)-4(x^2+2x+5).

My method for polynonimals is to write the x terms added together. Is there anything wrong with doing this?

That's how it should be done. x^2 +/- (Ax + Bx) +/- C. You have it right, the x terms should be combined.

Main content

Get ready for Algebra 2

Course: Get ready for Algebra 2 > Unit 1

Lesson 4: Multiplying binomials

Warmup: Multiplying binomials

Google Classroom

In this article we are going to get some initial practice with multiplying binomials, to prepare you for the Multiply binomials intro exercise.

If you don't know or remember the distributive property clearly enough, we recommend that you check out this lesson.

Example 1: Expanding $(x + 2) (x + 3)$ ‍

There are two ways we can think about this operation. Both are equally valid; you can use whichever you feel more comfortable with.

First method: Area model

We imagine a rectangle whose height is

x + 2

and width is

x + 3

, and divide it into four sub-rectangles:

Now we find the area of each sub-rectangle by multiplying its width and height:

Now we know that this is the area of the entire rectangle, which is the expression we are looking for:

x^{2} + 3 x + 2 x + 6

We can combine the

x

-terms to get a standard trinomial:

x^{2} + 5 x + 6

Second method: The distributive property

We can apply the distributive property twice to expand the expression:

\begin{aligned} (x + 2) (x + 3) \\ = (x + 2) x + (x + 2) 3 \\ = x \cdot x + 2 \cdot x + x \cdot 3 + 2 \cdot 3 \\ = x^{2} + 2 x + 3 x + 6 \\ = x^{2} + 5 x + 6 \end{aligned}

In any way, we reached the same result!

(x + 2) (x + 3)

expanded is

x^{2} + 5 x + 6

Check your understanding

Problem 1.1

Expand and combine like terms.

(x + 3) (x + 4) =

Example 2: Expanding $(x - 4) (x + 7)$ ‍

Why do we have another example? Well, multiplying binomials becomes a little more tricky when subtraction is involved. Let's see how it's done.

First method: Area model

As always, we draw a rectangle. However, don't forget to put a minus sign on the

4

Now we find the area of each sub-rectangle, keeping in mind that the height of the bottom-left rectangle is

- 4

, not

4

This doesn't make a lot of sense when thinking about actual rectangles and areas, but it works out with the algebra.

Now we add the areas of all the sub-rectangles:

\begin{aligned} x^{2} + 7 x + (- 4 x) + (- 28) \\ = x^{2} + 3 x - 28 \end{aligned}

Second method: The distributive property

We can apply the distributive property twice, making sure to remember that minus sign!

\begin{aligned} (x - 4) (x + 7) \\ = (x - 4) x + (x - 4) 7 \\ = x \cdot x + (- 4) \cdot x + x \cdot 7 + (- 4) \cdot 7 \\ = x^{2} - 4 x + 7 x - 28 \\ = x^{2} + 3 x - 28 \end{aligned}

Check your understanding

Problem 2.1

Expand and combine like terms.

(x - 2) (x + 5) =

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ethanlu
Posted 4 years ago. Direct link to ethanlu's post “Wait, does it really matt...”
Wait, does it really matter which order you put it in? For example, for the practice question I instead did x squared plus 15 -8x? or should I put it like x squared -8x plus 15? And if I do get it right, which is the most recommended?
Button navigates to signup pageComment on ethanlu's post “Wait, does it really matt...”
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- aker6549
  Posted 4 years ago. Direct link to aker6549's post “It does matter because th...”
  It does matter because the exponents the x^2 is larger than x and x is larger than the plain number
  Comment on aker6549's post “It does matter because th...”
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A HA HA Smart
Posted 4 years ago. Direct link to A HA HA Smart's post “Why can't we just use the...”
Why can't we just use the foil method instead. (First Outer, Inner, and Last
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(13 votes)
Answer
- David Severin
  Posted 4 years ago. Direct link to David Severin's post “It is better to know all ...”
  It is better to know all the methods so that you can expand what you can do. FOIL works great for (x+2)(x-4) but what if later on in math you have to multiply (x^2 + 2x - 3)(x + 5)? FOIL will not get you very far, but box method or distribution method will.
  Button navigates to signup page
  (23 votes)
henrymerino8
Posted 7 months ago. Direct link to henrymerino8's post “i got to the point where ...”
i got to the point where i can do on the top of my head now
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yummy algebraic soup :)
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j.mebitty
Posted 6 months ago. Direct link to j.mebitty's post “Isn't this just the FOIL ...”
Isn't this just the FOIL method? First, Outside, Inside, and Last. That mnemonic helped immensely with my understanding of multiplying polynomials.
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(11 votes)
Answer
- David Severin
  Posted 6 months ago. Direct link to David Severin's post “This is similar to FOIL, ...”
  This is similar to FOIL, but it is called the double distribution method, you distribute one of the binomials to all the parts of the other binomial. It is important to learn beyond FOIL because it is not limited to just binomials. You could do (x^2+2x+5)(x-4) using the distribution method. x(x^2+2x+5)-4(x^2+2x+5).
  Comment on David Severin's post “This is similar to FOIL, ...”
  (10 votes)
forceanty
Posted 4 years ago. Direct link to forceanty's post “My method for polynonimal...”
My method for polynonimals is to write the x terms added together. Is there anything wrong with doing this?
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(9 votes)
Answer
- Gabriel Jonas
  Posted 3 years ago. Direct link to Gabriel Jonas's post “That's how it should be d...”
  That's how it should be done.
  
  x^2 +/- (Ax + Bx) +/- C.
  
  You have it right, the x terms should be combined.
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  (11 votes)
xavien.torres
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Oh wow,took me a few min. to master this like nothing. Very helpful video!
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does it matter what order they are in?
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Get ready for Algebra 2

Course: Get ready for Algebra 2 > Unit 1

Example 1: Expanding (x+2)(x+3)‍

First method: Area model

Second method: The distributive property

Check your understanding

Example 2: Expanding (x−4)(x+7)‍

First method: Area model

Second method: The distributive property

Check your understanding

Want to join the conversation?

Example 1: Expanding $(x + 2) (x + 3)$ ‍

Example 2: Expanding $(x - 4) (x + 7)$ ‍