(n+2)^3

=n^3+3(n^2)(2)+3(n)(2^2)+2^3

=n^3+6n^2+12n+8

 

Could sum 1 tell me how this method cud b used for other exponents such as (n+2)^4 or (n+2)^5. So plz xplain to me this method of expanding, plz show the pattern if there is one.

Looking some stuff up on binomial expansion should reveal some ways it is used.

 

It basically considers expanding the brackets into its individual terms: i.e. ...

 

[math](a+b)^3 = (a+b)(a+b)(a+b) = a^3 + 3a^2b + 3ab^2 + b^3[/math]

 

To remember how its done, you realise that the number of terms will be a more than the power. I.e. in the example above, a power of 3 gives 4 terms.

 

The formula for each term when expanding [math](a+b)^n[/math] is [math]nCr * a^{n-r} * b^r[/math].

 

Where r is the term in the series (starting from 0). [math]nCr = \frac{n!}{r!*(n-r)!}[/math]

 

Applying this above to [math](a+b)^3[/math], to find the 2nd term its, [math]3C1 * a^{3-1} * b^1=3a^2b[/math]

 

Note the powers of a and b in each term always add up to n

wt dz the C stand for in that equation?

 

so for example if we take (n+2)^4,

 

we put it in the eqn:

 

4C0*n^4*2^0 = n^4

 

4C1*n^3*2^1 = 8n^3

 

4C2*n^2*2^2 = 16n^2

 

4C3*n^1*2^3 = 32n

 

4C4*n^0*2^4 = 64

 

= n^4+8n^3+16n^2+32n+64

 

Wouldnt you get this as an answer by following that formula. I know thats not correct so could u plz point out my mistakes. Duz the C mean to multiply the number infront of it by the number behind it.....or wtelse am i doing wrong.

 

Thx

You've almost got it except for the C bit. nCr is just a notation not a product, the C standards for combinations. You'll probably find nCr on a decent calculator next to nPr (permutations). If you do try entering 4 => nCr => 3 => ANS. You should get the answer 4.

 

To evaluate the co-efficient nCr you use the formula given above.

 

If you don't like using nCr, you can use Pascals triangle.

 

Have a look at this => http://www.davidscudder.com/pascal/binomial.html

The general term of the expansion :[math] nCr (a)^{n-r} (b)^r [/math]

oh The Rebel has mentioned it before.