Question 654549
Look at Row 5 in Pascals triangle: 1, 4, 6, 4, 1 


These are the coefficients to the terms


(2x)^4*(-3)^0
(2x)^3*(-3)^1
(2x)^2*(-3)^2
(2x)^1*(-3)^3
(2x)^0*(-3)^4


Note: you basically raise the first piece to the 4th power and the second piece to the 0th power. Then you count down on the first exponent and count up on the second exponent.


so we get 


1*(2x)^4*(-3)^0
4*(2x)^3*(-3)^1
6*(2x)^2*(-3)^2
4*(2x)^1*(-3)^3
1*(2x)^0*(-3)^4


which simplifies to


1*(16x^4)*(1)
4*(8x^3)*(-3)
6*(4x^2)*(9)
4*(2x^1)*(-27)
1*(1)*(81)


and that simplifies to


16x^4
-96x^3
216x^2
-216x
81


Now add up the terms to get 


16x^4 - 96x^3 + 216x^2 - 216x + 81


So 


(2x-3)^4 = 16x^4 - 96x^3 + 216x^2 - 216x + 81 for all values of x