Question

Expand (x1+2x2+3x3)4

Answer 1

really?

Answer 2

Expand (x1+2x2+3x3)4

Answer 3

to the power of four right?

Answer 4

yes

Answer 5

are these subscripts or superscripts?

Answer 6

\[(x_1+2x_2+3x_3)^4\]or \[(x^1+2x^2+3x^3)^4\]

Answer 7

subscripts

Answer 8

hesham, those trying to help you are not picking on you, but rather pointing out that your question is ambiguous. Satellite is trying to figure out what you mean.
Could you possibly use the Equation Editor? Lots of people here on OpenStudy could help you learn it.

Answer 9

\[x_1^4+8 x_2 x_1^3+12 x_3 x_1^3+24 x_2^2 x_1^2+54 x_3^2 x_1^2\]\[+72 x_2 x_3 x_1^2+32 x_2^3 x_1+108 x_3^3 x_1+216 x_2 x_3^2 x_1+144 x_2^2 x_3 x_1+16 x_2^4\]\[+81 x_3^4+216 x_2 x_3^3+216 x_2^2 x_3^2+96 x_2^3 x_3\]

Answer 10

lol wolfram strikes again!
http://www.wolframalpha.com/input/?i=%28x_1%2B2x_2%2B3x_3%29^4

Answer 11

actually i guess this has to do with elementary symmetric functions, but it will be torture in any case

Answer 12

If you don't want to use Equation Editor, then please at least indicate exponentiatin like this:

x^2 = x squared

(a+b)^2 = (a+b) squared

Answer 13

\[Expand (x1+2x2=3x3)^{4}\]

Answer 14

answer above

Answer 15

i want solution be using the multinomial theorem

Answer 16

step by step plz

Answer 17

Hesham, as a general rule we do NOT expand an equation such as (a+b=c)^4.
Are you positive that there's an " = " sign in there?

Are you familiar with "Pascal's Triangle"? I think that 's what you mean by "multinomial theorem." If not, please type out what "multinomial theorem" means, as I'm not familiar with it.

Answer 18

I'd suggest you do an Internet search for "Pascal's Triangle." That way you'll almost surely find examples of how to use this in expanding powers of binomials.

Answer 19

you know binomial theorem ?

Answer 20

binomial theorem for ( a + b)^3

Answer 21

multinomial theorem for ( a+b +c)^n

Answer 22

All right; thank you. If you have a "multinomial," such as (a+b+c)^4, you could still find a binomial expansion by grouping any two terms within the parentheses:

(a + [b+c])^2 does look like a binomial.
Without knowing precisely what you're learning in class and which methods of expansion you'reexpected to use, it's hard to advise you.

I still think you'd be well advised to look up and apply Pascal's Triangle for the expansion of powers of binomials.

Answer 23

ok thanks for you

Answer 24

Good luck. Hope you'll check out my suggestion that you look up Pascal's Triangle. One of your few remaining options would be to learn the formulas for
(a+b)^2
(a+b)^3
(a+b)^4

which are often listed in algebra textbooks.

Answer 25

(x1 + 2x2 + 3x3)
4 =

∑
n1+n2+n3=4

(
4

n1 , n2 , n3

)
xn11 (2x2)

n2(3x3)
n3

The number of terms in the above summation is given by(
4 + 3− 1
3− 1

)
=

(
6
2

)
=

6 · 5
2

= 15 .