And now I want to do a bunch

of examples dealing with probably the two most typical

types of polynomial multiplication that you’ll see,

definitely, in algebra. And the first is just

squaring a binomial. So if I have x plus 9 squared, I

know that your temptation is going to say, oh, isn’t that

x squared plus 9 squared? And I’ll say, no, it isn’t. You have to resist every

temptation on the planet to do this. It is not x squared

plus 9 squared. Remember, x plus 9 squared,

this is equal to x plus 9, times x plus 9. This is a multiplication of this

binomial times itself. You always need to

remember that. It’s very tempting to think that

it’s just x squared plus 9 squared, but no, you have

to expand it out. And now that we’ve expanded it

out, we can use some of the skills we learned in the last

video to actually multiply it. And just to show you that we can

do it in the way that we multiplied the trinomial last

time, let’s multiply x plus 9, times x plus a magenta 9. And I’m doing it this way just

to show you when I’m multiplying by this

9 versus this x. But let’s just do it. So we go 9 times 9 is 81. Put it in the constants’

place. 9 times x is 9x. Then we have– go switch to this

x term– we have a yellow x. x times 9x is 9x. Put it in the first

degree space. x times x is x squared. And then we add everything up. And we get x squared

plus 18x plus 81. So this is equal to x squared

plus 18x plus 81. Now you might see a little bit

of a pattern here, and I’ll actually make the pattern

explicit in a second. But when you square a binomial,

what happened? You have x squared. You have this x times this

x, gives you x squared. You have the 9 times

the 9, which is 81. And then you have this term

here which is 18x. How did we get that 18x? Well, we multiplied this x times

9 to get 9x, and then we multiplied this 9 times

x to get another 9x. And then we added the two

right here to get 18x. So in general, whenever you have

a squared binomial– let me do it this way. I’ll do it in very general

terms. Let’s say we have a plus b squared. Let me multiply it this way

again, just to give you the hang of it. This is equal to a plus b, times

a plus– I’ll do a green b right there. So we have to b times

b is b squared. Let’s just assume that this

is a constant term. I’ll put it in the b squared

right there. I’m assuming this is constant. So this would be a constant,

this would be analogous to our 81. a is a variable that we–

actually let me change that up even better. Let me make this into x plus b

squared, and we’re assuming b is a constant. So it would be x plus b, times x

plus a green b, right there. So assuming b’s a constant,

b times b is b squared. b times x is bx. And then we’ll do

the magenta x. x times b is bx. And then x times

x is x squared. So when you add everything,

you’re left with x squared plus 2bx, plus b squared. So what you see is, the end

product, what you have when you have x plus b squared, is

x squared, plus 2 times the product of x and b,

plus b squared. So given that pattern, let’s

do a bunch more of these. And I’m going to do

it the fast way. So 3x minus 7 squared. Let’s just remember

what I told you. Just don’t remember it, in the

back of your mind, you should know why it makes sense. If I were to multiply this

out, do the distributive property twice, you know you’ll

get the same answer. So this is going to be equal

to 3x squared, plus 2 times 3x, times negative 7. Right? We know that it’s 2 times each

the product of these terms, plus negative 7 squared. And if we use our product rules

here, 3x squared is the same thing as 9x squared. This right here, you’re going

to have a 2 times a 3, which is 6, times a negative 7,

which is negative 42x. And then a negative 7

squared is plus 49. That was the fast way. And just to make sure that I’m

not doing something bizarre, let me do it the slow

way for you. 3x minus 7, times 3x minus 7. Negative 7 times negative

7 is positive 49. Negative 7 times 3x

is negative 21x. 3x times negative 7

is negative 21x. 3x times 3x is 9 x squared. Scroll to the left

a little bit. Add everything. You’re left with 9x squared,

minus 42x, plus 49. So we did indeed get

the same answer. Let’s do one more, and we’ll

do it the fast way. So if we have 8x minus 3–

actually, let me do one which has more variables in it. Let’s say we had 4x squared plus

y squared, and we wanted to square that. Well, same idea. This is going to be equal to

this term squared, 4x squared, squared, plus 2 times the

product of both terms, 2 times 4x squared times y

squared, plus y squared, this term, squared. And what’s this going

to be equal to? This is going to be equal to

16– right, 4 squared is 16– x squared, squared, that’s 2

times 2, so it’s x to the fourth power. And then plus, 2 times

4 times 1, that’s 8x squared y squared. And then y squared, squared,

is y to the fourth. Now, we’ve been dealing with

squaring a binomial. The next example I want to show

you is when I take the product of a sum and

a difference. And this one actually comes

out pretty neat. So I’m going to do a very

general one for you. Let’s just do a plus

b, times a minus b. So what’s this going

to be equal to? This is going to be equal to a

times a– let me make these actually in different colors–

so a minus b, just like that. So it’s going to be this green

a times this magenta a, a times a, plus, or maybe I should

say minus, the green a times this b. I got the minus from

right there. And then we’re going to have the

green b, so plus the green b times the magenta a. I’m just multiplying every

term by every term. And then finally minus the green

b– that’s where the minus is coming from–

minus the green b times the magenta b. And what is this going

to be equal to? This is going to be equal

to a squared, and then this is minus ab. This could be rewritten as

plus ab, and then we have minus b squared. These right here cancel out,

minus ab plus ab, so you’re just left with a squared

minus b squared. Which is a really neat

result because it really simplifies things. So let’s use that notion to

do some multiplication. So if we say 2x minus

1, times 2x plus 1. Well, these are the

same thing. The 2x plus 1, you could view

this as, if you like, a plus b, and the 2x minus 1, you can

view it as a minus b, where this is a, and that b is 1. This is b. That is a. Just using this pattern that

we figured out just now. So what is this going

to be equal to? It’s going to be a squared, it’s

going to be 2x squared, minus b squared, minus

1 squared. 2x squared is 4x squared. 1 squared is just

1, so minus 1. So it’s going to be 4x

squared minus 1. Let’s do one more of these,

just to really hit the point home. I’ll just focus on

multiplication right now. If I have 5a minus 2b, and

I’m multiplying that times 5a plus 2b. And remember, this only applies

when I have at a product of a sum and

a difference. That’s the only time that

I can use this. And I’ve shown you why. And if you’re ever in doubt,

just multiply it out. It’ll take you a little

bit longer. And you’ll see the terms

canceling out. You can’t do this for just any

binomial multiplication. You saw that earlier in the

video, when we were multiplying, when we were

taking squares. So this is going to be, using

the pattern, it’s going to be 5a squared minus 2b squared,

which is equal to 25 a squared minus 4b squared. And, well, I’ll leave it there,

and I’ll see you in the next video.

Your use of colour is, in my mind, what stands out between your tutorials and those of others. This video is a good example of what works, though there could still be more colour used in a way that maintained the sensibility, and improved the understanding of students of the material.

F.O.I.L

i wish more teachers taught like this. the colors are awesome. its been a long time since i've been in school but this video is great! i wish i had this in school!

keep up the good work sir!

@kabooski First Out In Last

Thank you so much. I am currently going to an online college, and I haven't taken Algebra in years, watching you go through the problems enables me to better understand what it is that i am doing. thanks again =)

Good thing my teacher had your website on the whiteboard for several weeks…

FOIL FTW!

In the beginning of the video i was like hold on!! But then i remembered i could pause the video lol XD

WHAT THE HELL FOIL -_-

First

Outer

Inner

Last

FOIL !

2bx or not 2bx, that is the question!

Nice video, brings back memories I forgot. <g>

The method he is using is FOIL (First, Outer, Inner, Last)

Or …

Step 1 : Square of its first term .

Step 2 : Product of its terms.

Step 3 : Square of its last term.

Simple .

You're awesome.

Thanks!

Thanks for the tip

How about this…. (3-4m)² , (8-3x) (8+3x) , and (2t-1) (t+5) ??

PS: Can you solve this.. pretty please.??

Wow thank you soo much this was our next lesson and since now that I learned it in advance I probably wont have any problems with catching up in my class 😁😁 thanks so much

Where's the video on Factor Special Products (Basic)?

Example: x2−d=(x+6)(x+c)

how do you do this? 4(x+6)(x−5)

how about this cab you solve it (2a-7)(2a-7)

You cn also just 9x^2+2(x)(9)+9^2

thanks man our teacher didn't really teach us this and still gave it for homework so thank you

My teacher speaks math…

how?

you can also do this if the sign is plus:

1st step: Square the first term

2nd step: Multiply the 2nd term/last term by 2 and the multiply to the 1st term

3rd step: is to square the 2nd term/last term

The last example you did was too fast and didn't make sense [the (a+b)(a-b)]

How come the FOIL method wasn't used?

how do you do [x+5] [x-7]

help me please ..please

how to solve this?

(a-11)²

(2b+6)²

(3a²b-2b)²

(3/2mn+2)²

[(x+1)²-5)]²

thanks

keep sharing your knowledge

there are many people who needs your hlp keep doing it god bless

foil method will do

I need a vid about special products of polynomials😭

Wtf is Abab method?!?

this is literally just the FOIL method in a different name

👌🏼😁🌚🔥✖️😆😄⭐️

Hola

Oc Dawg XB!!!🎶🎵😂😂😂

i love you Sal, ur my hero

this video of 10 minutes is better than my professor of math like suscribe.

ı am turkey

You can use punnet square method for the first problem.

Very educational! thanks! 🙂

hi nerds

Do they write this with a mouse because damn that's amazing

OK this itches my head, isn't 9xsquared – 21x – 21x – 49 = 9x-49??????

Idk

Welcome to college😂

there are easier methods especially for special products but anyways, thanks!

FOIL METHOD AND VERTICAL METHOD AND HORIZONTAL METHOD…

My teacher teaches me this for 1 hour, and you teach me for only 10 minutes… And I understand your lesson more than my teacher 😂😂

Stop repeating words bro :3

Thank god i thought i had no chance of learning this

sal is on tv

Thank the LORD for Khan Academy…

thanks khan academy

what if its 20pm + 4n² + 20pm

will it be 44 n²pm²??

So it's foil?

thanks you have more information

Now i can pass the exam