Question

Expand and simplify using the binomial theorem (3x - 1)^4.

Answer 1

us pascal triangle

          1

        1   1

     1    2    1

   1    3    3    1

1     4    6    4    1  

each number is the sum of 2 above it and the 1's are on the outside because only 1 number is above them and its 1

so since its ^4 we use row 4 (actually the 5th because the top row is row zero)  

these at the coefficients

so here is

1a^4b^0-4a^3b^1+6a^2b^2-4a^1b^3+1a^0b^4

or easier to see it vertically

notices how exponential start a 4 and 0 until 4 goes down to 0 and 0 goes up to 4

(3x - 1)

a = 3x

b = -1

1a^4b^0  = 1(3x)^4(-1)^0

-4a^3b^1   =  -4(3x)^3(-1)^1

+6a^2b^2 ....

-4a^1b^3 .....

+1a^0b^4....

then write it horizontally

I think you see now,  when you expand this you will have your answer