Main content

## Algebra (all content)

### Unit 10: Lesson 7

Special products of binomials- Special products of the form (x+a)(x-a)
- Squaring binomials of the form (x+a)²
- Multiply difference of squares
- Special products of the form (ax+b)(ax-b)
- Squaring binomials of the form (ax+b)²
- Special products of binomials: two variables
- More examples of special products
- Polynomial special products: perfect square
- Squaring a binomial (old)
- Binomial special products review

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# Squaring a binomial (old)

An old video where Sal expands and simplifies (7x+10)². Created by Sal Khan and Monterey Institute for Technology and Education.

## Video transcript

We're asked to simplify
7x plus 10 squared. And your temptation when you see
something like this might be to just make it 7x squared
plus 10 squared and that would be incorrect. Remember, when you're squaring
something, you're multiplying something by itself. So this wouldn't be 7x squared
plus 10 squared. This is equal to 7x plus
10 times 7x plus 10. This is not equal to-- sometimes
if you said this is 7x times 10 squared, then you
could say this is equal to 7x squared times 10 squared. You would be able to do it in
this situation right here. But that's not what's
going on here. This is 7x plus 10 squared,
which is just 7x plus 10 times 7x plus 10. So let me delete
that up there. That's probably the single
biggest point of confusion when people first learn
to take a square of an expression like this. So always remember that it's 7x
plus 10 times 7x plus 10. And now we can multiply
it out. So one, we could distribute this
yellow 7x plus 10 onto each of the terms into
the green one. So it would be 7x plus 10
times 7x right here. So we put the 7x out front. And then we could say plus
7x plus 10 times 10. Or we could say plus 10
times 7 x plus 10. I just distributed the 7x plus
10 on each of these terms. Then you do the distributive
property again. 7x times 7x is 49x squared. 7x times 10 is 70x. And then you have 10 times
7x is another 70x. And then you have 10 times
10, which is 100. Now, there's something
interesting you might want to notice right now is that this
expression, it is the first expression squared, right? 7x, the whole expression
squared is 49x squared. And then you do have your
last expression squared, 10 squared is 100. But then in between, you have
the product of these two things twice, and that's just
a byproduct of having to do all of the different
combinations of products. So the end expression, when you
simplify everything, it becomes 49x x squared
plus 140x plus 100. So if you want to remember
a quick way of squaring a binomial like this, and just
remember, it is coming out of this distributive property, but
if you had to do it really fast, it's just going to be this
first term squared, which is that right there, plus 2
times the product of these two terms. 7x times 10 is 70x,
and then you multiply it by 2, you get 140x. You get that right there. And then the last term is just
going to be the square of the second term right there. 10 squared is 100.