I need help with algebra problem?

Question

i need help with this problem (x/2-2w)^5 it is going to have six terms, but i dont how to do it.. someone please help, it deals with the binomial theorem

Answer 1

It does deal with the binomial theorem which gives the expansion of binomials raised to a power:

(a + b)^n

The expansion has n+1 terms, and the coefficients of these terms are called binomial coefficients. There are several symbols used for these.

In your problem, let a = x/2 and b = -2w, and the expansion is (for n = 5)

(5,0)*a^5 + (5,1)*a^4*b + (5,2)*a^3*b^2 + (5,3)*a^2*b^3 + (5,4)*a*b^4 + (5,5)*b^5.

You can get more information here http://en.wikipedia.org/wiki/Binomial_theorem
and values for the coefficients here:http://en.wikipedia.org/wiki/Binomial_coefficients

Specifically note Pascal's Triangle which organizes the values of these coefficients. For your binomial to the 5th power the coefficients are

(5,0) = 1; (5,1) = 5; (5,2) = 10; (5,3) = 10; (5,4) = 5; (5,5) = 1

Plug the numbers into the expansion to get the final result.

As a hint I will give you the value of the third term: (5,2)*a^3*b^2 = 10*(x/2)^3*(-2w)^2 = 10*x^3/8*4w^2 = 5*x^3*w^2