Question

Expand (2x-3y)^4 using Pascal's Triangle. Show work

Answer 1

(2x+3y)⁴
1) let 2x = a   and 3y = b

(a+b)⁴ = a⁴ + a³b + a²b² + ab³ + b⁴
Now let's find the coefficient of each factor using Pascal Triangle
     
                     0     |               1
                     1     |            1    1
                     2     |          1   2   1
                     3     |         1  3   3   1
                     4     |       1  4   6    4  1

0,1,2,3,4,.. represent the exponents of binomials 
Since our binomial has a 4th exponents, the coefficients are respectively:

(1)a⁴ + (4)a³b + (6)a²b² + (4)ab³ + (1)b⁴
Now replace a and b by their real values in (1):

2⁴x⁴ +(4)8x³(3y) + (6)(2²x²)(3²y²) + (4)(2x)(3³y³) + (1)(3⁴)(y⁴)

16x⁴ + 96x³y + 216x²y² + 216xy³ + 81y⁴