Question

2a +3ba^2 + 2ab^2 +b^3
how can I get (a+b) (2a^2 +ab + b^2)?

Answer 1

you seem to be missing something

Answer 2

what am I missing?

Answer 3

well, your factored form has 2a^3, but you have no 2a^3 to start with

Answer 4

it has 2a^2

Answer 5

a*2a^2 = 2a^3 which isnt in your starting stuff

Answer 6

thats because its factorized. If I combine the factors I get above but I am not sure how to get to the factor part

Answer 7

im saying, when you combine your factors, you get 2a^3 ... you have no 2a^3 to start with so one doesnt form into the other

Answer 8

you are missing something

Answer 9

ooo sorry my bad, it suppose to be 2a^3 the 2a

Answer 10

if factor by grouping is your cup o tea, then we want to split it into 6 terms, but grouping is not what im good at

Answer 11

I'm trying to do that but I am not getting the same as the factor

Answer 12

im att a(2a^2+2b^2) + b(3a^2 + b^2) which is near close to the factor

Answer 13

2a^3 +3ba^2 + 2ab^2 +b^3

2a^3 +(2ba^2 + ba^2) + (i ab^2+j ab^2) +b^3

(2a^3 +2ba^2 + i ab^2) + (ba^2+j ab^2 +b^3)

a(2a^2 +2ba + i b^2) + b(a^2+j ab +b^2)

i loathe by grouping ....

Answer 14

2a^3 +3ba^2 + 2ab^2 +b^3

2a^3 +(x ba^2 + y ba^2) + (i ab^2 +j ab^2) +b^3

(2a^3 +x ba^2+ i ab^2) + (y ba^2 +j ab^2 +b^3)

a(2a^2 +x ba+ i b^2) + b(y a^2 +j ab +b^2)

y = 2
i = 1
x = j

x+y = 3, x = 1
i + j = 2, j = 1

Answer 15

but but I don't see (a+b)(2a^2+ab+b^2) =.= my goal is to just reach that factor

Answer 16

since the left and right terms need to be the same, we can solve for how we need to split them

Answer 17

without knowing how to split it, i just used xyij as placeholders to get to:

a(2a^2 +x ba+ i b^2) + b(y a^2 +j ab +b^2)

now:

2a^2 +x ba+ i b^2
= y a^2 +j ab + b^2
y=2 x=j i=1 , this is the only way itll work for us

x+y = 3, and i+j = 2
x+2 = 3, and 1+j = 2
x=1 j=1

Answer 18

soo, let fill those in:

2a^3 +3ba^2 + 2ab^2 +b^3

2a^3 +(1 ba^2 + 2 ba^2) + (1 ab^2 +1 ab^2) +b^3

(2a^3 +ba^2+ ab^2) + (2ba^2 +ab^2 +b^3)

a(2a^2 +ba+ b^2) + b(2a^2 +ab +b^2)

(a+b) (2a^2 +ba+ b^2) , as required

Answer 19

\[2a^3+3ba^2+2ab^2+b^3\] Which methods would you use to factor this? the easiest (I might of picked the hardest lol)

Answer 20

your pick was fine, otherwise theres a few trial and errors to mess with

Answer 21

what about one where I don't have to deal with other terms?

Answer 22

got an example?

Answer 23

or a method that doesnt deal with new terms ...

Answer 24

like as how you used x j i y etc

Answer 25

if we assume (a+b) is a factor, which at first glance it may not be, then division finds the other factor

Answer 26

2a^2 + ab + b^2
---------------------------
a+b | 2a^3 +3ba^2 + 2ab^2 +b^3
-(2a^3 +2ba^2)
------------
ba^2 +2ab^2
-(a^2b + ab^2)
-------------
ab^2 + b^3
-(ab^2 + b^3)
------------
0

Answer 27

but there is not way to know if a+b is a factor to start with

Answer 28

well, there is, let b=-a if it zeros out then (a+b) is a factor

Answer 29

2a^3 +3(-a)a^2 + 2a(-a)^2 +(-a)^3

2a^3 -3a^3 + 2a^3 - a^3 = 4-4 = 0

Answer 30

so (a+b) is a factor

Answer 31

this is way easier than the first part, thanks you.

Answer 32

wait how did you start with b = -a?

Answer 33

at this point, there is no 'easier' way to me

Answer 34

well, if (a+b) is a factor: then f(x) = (a+b)(whatever) is our factorization

when (a+b) = 0, then the original f(x) will have to equal 0

a+b = 0 when b=-a, or when a=-b doesnt matter

Answer 35

knowing that it is a factor, we can do the division to find the (whatever) part

Answer 36

ooo ok so I can know if those are factors of the function if they are equals to 0

Answer 37

this would only be easy if we had terms such as a and b right?

Answer 38

maybe

Answer 39

ok, I think I got the hang of it. thanks

Answer 40

good luck :)