1
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f of x is equal to 7x minus 5

2
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g of x is equal to x to the third power plus 4x

3
00:00:08,478 --> 00:00:13,788
and then they ask us to find f times g of x

4
00:00:13,788 --> 00:00:18,882
so the first thing to realize is that this notation, f times g of x,

5
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is just referring to a function that is the product of f of x and g of x

6
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so by definition, this notation just means f of x times g of x

7
00:00:30,900 --> 00:00:35,138
and then we just have to substitute f of x with this definition and g of x with this definition

8
00:00:35,138 --> 00:00:38,862
and then multiply out these algebraic expressions

9
00:00:38,862 --> 00:00:44,810
so f of x is right over there and g of x is right over there

10
00:00:44,810 --> 00:00:46,403
so lets do it

11
00:00:46,403 --> 00:00:56,292
so this is going to be equal to, switch back to the orange color, is going to be equal to f of x which is 7x minus five times g of x

12
00:00:56,292 --> 00:01:03,595
and g of x is x to the third power plus 4x

13
00:01:03,595 --> 00:01:10,071
and you could, if we were multiplying two expressions that each have two terms, you could use FOIL if you like

14
00:01:10,071 --> 00:01:14,490
i don't like using FOIL becuase you might forget what it's even about

15
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FOIL is really just using the distributive property twice

16
00:01:18,452 --> 00:01:21,900
so, for example, you take this expression, whatever you have out here

17
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if you had a 9 out here or an "a" or an "x" or anything, now you have 7x minus 5

18
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if your multipling it times this expression you would multiply this times each term over here

19
00:01:32,333 --> 00:01:35,898
so when you multuply 7x minus 5 times x to the third

20
00:01:35,898 --> 00:01:42,518
you get, and i'll write it this way, you get x to the third times, acutally let me write it the other way

21
00:01:42,518 --> 00:01:59,615
you get 7x minus five times x to the third and then you have plus 7x minus 5 times 4x

22
00:01:59,615 --> 00:02:02,379
and now we can do the distributive property again

23
00:02:02,379 --> 00:02:06,821
we're not normally used to seeing the things we distributed on the right hand side but it's the same exact idea.

24
00:02:06,821 --> 00:02:08,611
we could put x to the third here as well

25
00:02:08,611 --> 00:02:14,390
now when we distribute, you multiply x to the third times 7x and times negative 5

26
00:02:14,390 --> 00:02:20,036
x to the third times 7x is 7x to the fourth power

27
00:02:20,036 --> 00:02:24,438
x to the third times negative 5 is minus 5x to the third

28
00:02:24,438 --> 00:02:33,667
and then you do it over here, you distribute the 4x times 7x is plus 28x squared

29
00:02:33,667 --> 00:02:39,819
4x times negative 5 is minus 20x

30
00:02:39,819 --> 00:02:41,549
and lets see if we can simplify this

31
00:02:41,549 --> 00:02:47,203
we only have one fourth degree term, one third degree term, one second degree term, and one first degree term

32
00:02:47,203 --> 00:02:49,256
so actually you can't simplify this anymore and we're done!

33
00:02:49,256 --> 00:02:52,472
this is the product of those two function definitions

34
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this is f times g of x. it is a new function created by multiplying the other two functions.