Question

simplify -x^3+2x(x-x^2)

Answer 1

pretty much like the last one
distribute the \(2x\) first
then combine like terms

Answer 2

need help doing it?

Answer 3

would i distribute it to the numbers in the parenthesis?

Answer 4

yes

Answer 5

let me know what you get

Answer 6

so the
2x(x-x^2)
would be
2x^2-x^2?
so that'd just be 2? bc like terms

Answer 7

not quite
the \(2x^2\) part is right, but \(2x\times (-x^2)=-2x^3\)

Answer 8

multiplying like that has nothing to do with 'like terms' it is only when you add or subtract that you combine like terms

Answer 9

so -x^3+(-2x^3)? or more?

Answer 10

like terms?

Answer 11

yes you can always multiply
for example \(x\times x^2=x^3\) but when you add you can only add like terms for example
\[x+3x=4x\] but you cannot add \(x+3x^2\)

Answer 12

you know what i mean by like terms? same variable, same exponent

Answer 13

lets do this from the beginning
\[ -x^3+2x(x-x^2)\] multiply using the distributive property
\[-x^3+2x\times x+2x\times (-x^2)\]
\[-x^3+2x^2-2x^2\]

Answer 14

then the "like terms" as \(-x^3\) and \(-2x^3\) but not the \(2x^2\)

Answer 15

combining them gives
\[-3x^3+2x^2\]

Answer 16

Yeah, we learned like terms today

Answer 17

it is clear if you think about adding numbers
for example
\[200=2\times 10^2,400=4\times 10^2\] and
\[200+400=600=6\times 10^2\]

Answer 18

so like for example, 5-x+2? How would that be done since it has no like terms? would I do stay change change and turn it to 5+(-x)+2 and then so 7+(-x)?

Answer 19

like saying \(2x^2+4x^2=6x^2\)

Answer 20

yes the numbers with no variables (constants) are also like terms, so of course you can add them or subtract them

Answer 21

and your answer is correct, \(7+(-x)\) although you would probably write \(7-x\)
same thing, just like \(10+(-4)=10-4\)

Answer 22

ok I actually think I understand now

Answer 23

you got another one we can try? or are you done

Answer 24

I could check one, just one second

Answer 25

k

Answer 26

8b+5-3b

Answer 27

So I would add 8b and 5?
to make 13b-3b?

Answer 28

no you cannot add \(8b\) and \(5\) since you don't know what \(b\) is
but you can subtract \(8b-3b\)

Answer 29

oh oops looked at that wrong

Answer 30

suppose \(b\) as a \(\$100\) bill
then you would have \(8\) \(\$100\) bills and then \(-3\) \($100\) bills leaving you with \(5\) \(\$100\) bills

Answer 31

but that number \(5\) just stays there, because you have no other numbers to add or subtract

Answer 32

so how would I simplify that? like step by step?

Answer 33

\[8b+5-3b
\] lets group the like terms together
\[8b-5b+5\]
now all that is left to do is find \(8b-3b\)

Answer 34

hope it is clear that \(8b-3b=5b\) just like 8 million dollars minus 3 million dollars is 5 million dollars, and 8 bottle of beer minus 3 bottles of beer is 5 bottles of beer

Answer 35

so final answer is
\[5b+5\]
that number 5 has no match, no other number to combine it with, so it just sits there

Answer 36

ooookay now I get that one

Answer 37

finally done with simplifying

Answer 38

btw there is no such mathematical operation as "simplify"
it is the lazy math teacher's way of saying "give me the answer i want to see"
what you are doing is combining like terms

Answer 39

hope you get it well, because it is kind of important

Answer 40

laughing so hard at that bc its so true

Answer 41

sometimes "simplify" means
\[\frac{12}{8}=\frac{3}{2}\] which is really "reduce to lowest terms"
you see that has nothing to do with what you are doing

Answer 42

sometimes it means \(\sqrt{50}=5\sqrt{2}\)
math teachers can say it to mean almost anything

Answer 43

thank you sooooooo much

Answer 44

yw