a. (x -3)4 = x4 + 4.x3.(-3) +6.x2.(-3)2 +4.x.(-3)3 + (-3)4
= x4 -12.x3 +54.x2 - 108.x +81.
b. (3x - 2y)4 = (3x)4 + 4.(3x)3(2y) + 6.(3x)2.(2y)2 + 4.(3x).(2y)3 + (2y)4
= 81x4 + 216x3y + 216x2y2 + 96xy3 + 16y4
c. (x+5)4 + (x - 5)4 = (x5+ 5x4.5 + 10x3.52 + 10x2.53 +5x.54+ 55) + (x5+ 5x4.(-5) + 10x3.(-5)2 + 10x2.(-5)3 + 5x.(-5)4+ (-5)5)
= 2x5 + 500x3 + 6250x
d. (x - 2y)5 = x5 +5x4(2y) + 10x3(2y)2 + 10x2(2y)3 +5x(2y)4 + (2y)5
= x5 +10x4y + 40x3y2 + 80x2y3 + 80xy4 + 32y5.