A. maths(F.4) Bionomial theorerm

Expand (2-x)5(2x-3)4 in descending powers of x as far as the term in x7.

(2-x)5(2x-3)4
= -(x-2)5(2x-3)4

(x-2)5
= x5 + 5x4(-2) + (5*4/2)x3(-2)2 - …..
= x5 - 10x4 + 40x3 + ….

(2x-3)4
= (2x)4 + 4(2x)3(-3) + (4*3/2)(2x)2(-3)2 + ….
= 16x4 – 96x3 + 216x2 + ….
所以
-(x-2)5(2x-3)4
= -{[1*16]x9 + [1*(-96)+(-10)(16)]x8 + [1*216+(-10)(-96)+(40)(16)]x7+…
= -{16x9 – 256x8 + 1816x7 + …..
= -16x9 + 256x8 - 1816x7 + …..