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## Algebra 1

# Warmup: Multiplying binomials

CCSS.Math:

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 left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, plus, 3, right parenthesis

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, plus, 2 and width is x, plus, 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:

We can combine the x-terms to get a standard trinomial:

### Second method: The distributive property

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

In any way, we reached the same result! left parenthesis, x, plus, 2, right parenthesis, left parenthesis, x, plus, 3, right parenthesis expanded is x, squared, plus, 5, x, plus, 6.

## Check your understanding

## Example 2: Expanding left parenthesis, x, minus, 4, right parenthesis, left parenthesis, x, plus, 7, right parenthesis

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 minus, 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:

### Second method: The distributive property

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

## Check your understanding

## Want to join the conversation?

- 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?(17 votes)
- It does matter because the exponents the x^2 is larger than x and x is larger than the plain number(22 votes)

- Why can't we just use the foil method instead. (First Outer, Inner, and Last(10 votes)
- 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.(21 votes)

- My method for polynonimals is to write the x terms added together. Is there anything wrong with doing this?(9 votes)
- That's how it should be done.

x^2 +/- (Ax + Bx) +/- C.

You have it right, the x terms should be combined.(10 votes)

- Oh wow,took me a few min. to master this like nothing. Very helpful video!(13 votes)
- i got to the point where i can do on the top of my head now(11 votes)
- does it matter what order they are in?(8 votes)
- so do we use the FOIL method?(6 votes)
- That is one way to do it. Double distribution or box method is two additional ways. FOIL has its limits to multiplying two binomials, so you need more if you multiply a trinomial by a binomial later on.(3 votes)

- it feels so weird not doing the problems on paper(7 votes)
- if the signs are all negative.should the answer be in negative(4 votes)
- when adding negative the answer will be negative when multiplying a negative with a positive you will always get a negative when multiplying 2 negatives you will always get a positive.(5 votes)

- does it matter what order they are in?(3 votes)
- Technically, not it does not matter what order you put them in as long you properly proceed with the Order of Operations. However, it is probably the best practice to the terms in Polynomial standard form, which is when you write each term in order from highest degree first (or highest exponent value) to lowest degree last (or lowest exponent value).
**Here's a video to help you out more**:

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratics-multiplying-factoring/x2f8bb11595b61c86:multiply-monomial-polynomial/v/polynomials-intro(6 votes)