Name: Multiplying monomials | Polynomial arithmetic | Algebra 2 | Khan Academy
Uploaded: 2020-03-27T17:37:43.000Z
Duration: 3 min 16 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

- [Instructor] Let's say that we wanted to multiply

five x squared and, I'll do this in purple,

three x to the fifth, what would this equal?

All right, now let's work through this together.

if we're just multiplying a bunch of things,

it doesn't matter what order we multiply them in.

So you can just view this as five times x squared

or we could multiply our five and three first,

so you could view this as five times three, times three,

times x to the fifth, times x to the fifth.

Now what is x squared times x to the fifth?

that exponent properties would come into play here.

so we have the some base and different exponents,

that this is going to be equal to x to the,

x to the two plus five power, or x to the seventh power.

If what I just did seems counterintuitive to you

That is x times x times x times x times x.

And if you multiply them all together what do you get?

five x squared times three x to the fifth

So the key is, is look at these coefficients,

look at these numbers, a five and a three, multiply those,

you have x here, so you have a common base,

and what we just did is known as multiplying monomials,

which sounds very fancy, but this is a monomial, monomial,

where we have multiple of these things added together.

But that's all it is, multiplying monomials.

and let's use a different variable this time,

Pause this video and see if you can work through that.

All right, so I'm gonna do this one a little bit faster.

I am going to look at the three and the negative four

once again they're both the variable t as our base,

times t to the first power, that's what t is,

that's going to be t to the seven plus one power,

we just multiplied another set of monomials.

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Multiplying monomials | Polynomial arithmetic | Algebra 2 | Khan Academy

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