Question

How would I simplify 8x^2y/4xy

Answer 1

well lets see ...

\[8x ^{2}y/xy\]

does 4 go into 8? how many times?
does x go into x²? how many times?
does y go into y? how many times?

Answer 2

Yes 4 goes into 8, 2 times

Answer 3

forgot the 4 in the denominator sorry :)

Answer 4

but okay yes 2 times...now the x's? what do you do when dividing exponents? subtract the exponents....so

x² / x

can be seen as

x² - x^1

what is x^2 - x^1?

Answer 5

*subtract the exponents :) *

Answer 6

2-1 which is 1

Answer 7

exactly...so x^1...(can also just be written as x right) (anything to the 1 power is just that number right?)

okay ...so ...the y's...

y / y = ?

Answer 8

1?

Answer 9

perfect :) dont put the ? afterwards you know it :)

okay

so we have

(4 into 8, 2 times)
x into x² , 2 times..and we have x left right?
y into y...once)

to simplify ...put what we have

2x would be your simplification

Answer 10

Awesome! thank you. Could you help me with one more?

Answer 11

absolutely ...if i can :)

Answer 12

Emily's garden is (x + 4) feet wide and (2x − 3) feet long. She knows the area of her garden is the length times the width. What is the area of her garden?

Answer 13

btw you're really good at math!

Answer 14

why thank you for the compliment :)

okay...area DOES = length times width in this case
so

(x+4) times (2x -3)

can be written as

(x+4)(2x-3)

have you learned the foil method yet?

Answer 15

Yes I have, I actually do online schooling I'm in 9th grade

Answer 16

ahh...excellent...so then use foil to simplify

(x+4)(2x-3)

what do you get?

Answer 17

So I would do x*2x, and than 4x3?

Answer 18

you would do

x*2x
x*-3
4*2x
4*-3

Answer 19

the x*2x always confuse me

Answer 20

I guess it's the variable that throws me off

Answer 21

the foil method says...you take the first term in the first parenthesis...and multiply it by EVERY term in the second parenthesis....then....you take the second term in the first parenthesis and multiply it by every term in the second parenthesis...just a refresher :)

Answer 22

and okay....remember what i said what we do when DIVIDING exponent? what do we do?

Answer 23

subtract?

Answer 24

right....so when we multiply exponents.....we add...the opposite of division....is multiplication... the opposite of subtraction ...is addition :)

Answer 25

so ..if we have x * 2x

can be written as x^1 * 2x^1

what do we have?

Answer 26

So I would multiply those two?

Answer 27

you multiply x and 2x....but
when written as

x^1 * 2x^1

this is muliplying exponents.....so we ADD the exponents

Answer 28

Oh okay, so 1+1=2

Answer 29

exactly....so we have 2x^2 right??

Answer 30

Yes

Answer 31

alright..now finish the foil method

Answer 32

I'm sorry what am I finishing?

Answer 33

lol...the foil method

x*2x (you did this step)
x*-3 (what is this one?)
4*2x
4*-3

Answer 34

Sorry math isn't my best subject. So x*-3 so -2? does that x stand for 1?

Answer 35

no x is just x......
and dont worry you're doing great! :)

x times -3

is -3x..just combine the two :)

alright now you did

x*2x (you did this step 2x²)
x*-3 (did this one...-3x)
4*2x (what is this one?)
4*-3

Answer 36

8x?

Answer 37

perfect :) see you're doing great!

now

x*2x (you did this step 2x²)
x*-3 (did this one...-3x)
4*2x (did this one...8x)
4*-3 (what is this one?)

Answer 38

1?

Answer 39

what is 4 times -3? (not adding)

Answer 40

sorry -12

Answer 41

perfect..you have all you need :)
so we have

2x² -3x +8x -12

(hint...-3x and 8x can be combined....what is -3 + 8?)

Answer 42

5

Answer 43

perfect...our final answer is

2x² + 5x - 12

you cannot combine x² with anything other than another x²
you cannot combine x with anything other than another x
you cannot combine a number with anything other than another number

so no more simplifying...that is your answer :)

Answer 44

Awesome! Thank you so much. I appreciate all the help. You make it seem really easy!

Answer 45

no problem :) again you did all the work...i just made the steps one after another for you to follow....practice more of these and it'll become second nature...i've been doing equations like these since 9th grade as well...so 5 years now...second nature :)

Answer 46

Well you're very good at them! I can tell! I think that's all the questions I have for now. Thank you John!

Answer 47

not a problem :) like i said...anytime :)

Answer 48

Where are you from? I am from Ohio

Answer 49

i never realized you replied to this again...lol sorry...i am from Massachusetts