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We're asked to simplify 7x plus 10 squared.

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And your temptation when you see something like this might

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be to just make it 7x squared plus 10 squared and that would

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be incorrect.

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Remember, when you're squaring something, you're multiplying

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something by itself.

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So this wouldn't be 7x squared plus 10 squared.

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This is equal to 7x plus 10 times 7x plus 10.

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This is not equal to-- sometimes if you said this is

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7x times 10 squared, then you could say this is equal to 7x

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squared times 10 squared.

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You would be able to do it in this situation right here.

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But that's not what's going on here.

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This is 7x plus 10 squared, which is just 7x plus 10 times

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7x plus 10.

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So let me delete that up there.

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That's probably the single biggest point of confusion

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when people first learn to take a square of an

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expression like this.

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So always remember that it's 7x plus 10 times 7x plus 10.

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And now we can multiply it out.

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So one, we could distribute this yellow 7x plus 10 onto

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each of the terms into the green one.

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So it would be 7x plus 10 times 7x right here.

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So we put the 7x out front.

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And then we could say plus 7x plus 10 times 10.

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Or we could say plus 10 times 7 x plus 10.

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I just distributed the 7x plus 10 on each of these terms.

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Then you do the distributive property again.

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7x times 7x is 49x squared.

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7x times 10 is 70x.

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And then you have 10 times 7x is another 70x.

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And then you have 10 times 10, which is 100.

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Now, there's something interesting you might want to

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notice right now is that this expression, it is the first

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expression squared, right?

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7x, the whole expression squared is 49x squared.

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And then you do have your last expression squared,

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10 squared is 100.

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But then in between, you have the product of these two

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things twice, and that's just a byproduct of having to do

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all of the different combinations of products.

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So the end expression, when you simplify everything, it

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becomes 49x x squared plus 140x plus 100.

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So if you want to remember a quick way of squaring a

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binomial like this, and just remember, it is coming out of

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this distributive property, but if you had to do it really

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fast, it's just going to be this first term squared, which

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is that right there, plus 2 times the product of these two

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terms. 7x times 10 is 70x, and then you multiply it

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by 2, you get 140x.

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You get that right there.

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And then the last term is just going to be the square of the

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second term right there.

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10 squared is 100.

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