Question

please explain how to do this !!

"For each given pair of functions, multiply or divide as instructed. Be sure to show all the steps
required to write your answer in simplest form. "

f(x) = 2x
g(x) = 3x^3

i know how to combine the two, i think ? im guessing that combined they are 2x * (3x^3). correct me if im wrong, and please help me distribute and simplify !

Answer 1

when you multiply same variables you should add their exponents
\[\huge\rm x^m \times x^n = x^{ m \times n }\]

Answer 2

f(x) times g(x)
replace f(x) and g(x) by their values then multiply

Answer 3

okay ... so i multiply 2x and 3x^3 ? that would be 6^3, right ?

Answer 4

6^3 ?? 6 power 3 ?

Answer 5

when you multiply variables with SAME bases then add their exponent like in this exponent rule x^m times x^n both bases are same so x^{m+n}

Answer 6

you can ask question if you don't get it :-)

Answer 7

sorry i had to do something else for my mom and then i was trying to figure it out. i dont quite understand yet though. what do i do with the coefficient ?

Answer 8

multiply them together
2x times 3x^3
2 times 3
x times x^3

Answer 9

oooh okay !!! so,
2 * 3 = 6.
and
x * x^3 = x^3, right ?
now do i combine those answers ?

Answer 10

like i said when you multiply same variables you should add their exponent
and remember x is raising to the one power

Answer 11

\[\large\rm x^1 \times x^3 \]
apply exponent rule

Answer 12

oh right, sorry :PP i completely forgot that, haha
so i wouldnt 'multiply' per say, id add, and it would be x^4 ??

Answer 13

yep!

Answer 14

great, okay ! is the next step to combine the answers ?

Answer 15

are there any like terms ??

Answer 16

no, there isnt i dont think ! is that the answer ??

Answer 17

yep

Answer 18

btw after multiplying is there any term left to combine
2 times 3
x^1 times x^3 = x^4
6x^4
i separated these so you can understand :-)

Answer 19

thank you so much for your help

Answer 20

no problem do you have to divide that ?

Answer 21

no i dont, thank you though : ))

Answer 22

nice! my pleasure :-)