f of x is equal to 7x minus 5. g of x is equal to x to

the third power plus 4x. And then they ask us to find f

times g of x So the first thing to realize is that this

notation f times g of x is just referring

to a function that is a product of f

of x and g of x. So by definition, this notation

just means f of x times g of x. And then we just

have to substitute f of x with this definition,

g of x with this definition, and then multiply out these

algebraic expressions. f of x is right over there. And g of x, is right over there. So let’s do it. So this is going to be

equal to– switch back to the orange color. It’s going to be

equal to f of x, which is 7x minus 5

times g of x, and g of x is x to the

third power plus 4x. And you could– we’re

multiplying two expressions that each have two terms. You could use FOIL if you like. I don’t like using

FOIL because you might forget what

it’s even about. Foil is really just using the

distributive property twice. So for example, you

take this expression. Whatever you have out here,

if you had a 9 out here, or an a, or an x, or anything. Now you have 7x minus 5. If you’re multiplying it

times this expression, you would multiply this

times each term over here. So when you multiply 7x

minus 5 times x to the third, you get– I’ll

write it this way. You get x to the third times–

actually, let me write it the other way. You get 7x minus 5

times x to the third. And then you have plus

7x minus 5 times 4x. And now we can do the

distributive property again. We’re not normally

used to seeing the things we distribute

on the right hand side. It’s the same exact idea. We could put the x to

the third here as well. And when we distribute,

you multiply x to the third times 7x

and times negative 5. x to the third times 7x

is 7x to the fourth power. X to the third times negative

5 is minus 5x to the third. And then you do it over here. You distribute the

4x over the 7x. 4x times 7x is plus 28x squared. 4x times negative

5 is minus 20x. And let’s see if we

can simplify this. We only have one fourth degree

term, one third degree term, one second degree term,

and one first degree term. Actually, we can’t

simplify this anymore. And we’re done. This is the product of those

two function definitions. This is f times g of x. It is a new function created

by multiplying the other two functions.

first

second

third

Fish

this is completely wrong u noob get rekt nerd

what happens if you f(x)=7+10/x

wow there's one dislike wtf

explained clear and fast…thanks

How's x^3 * 7x = 7x^4? Edit I just found out how it because multiply and yeah 7x PLUS x is 8x but with multiplying its not the same and there for x^3 * 7x = 7x^4 is right beacouase when its to the 4th power instead of 3rd you multiply 1 more time with x

should have explained it more thoroughly. I dont get why u separated the problem like that

In 2:14

Why x^3 * 7x = 7x^4 !

Why there's fourth power. I can't get it 🙁