The Binomial Expansion

Coach Name: Sir Muhammad Abdullah Shah

Edexcel IAL /P2 /June 2019/Q4 (Binomial Expansion)

  • Find the first four terms, in ascending powers of x, of the binomial expansion of​​ 

2-14x6

(4)

  • Given that x is small, so terms in x4​​ and​​ higher power of x may be ignored, show

2-14x6+ 2+14x6=a+bx2

Where a and b are constant to be found.​​ 

(3)

SOLUTION​​ 

a-​​ Using binomial theorem to find the first 4 terms of the expression.​​ 

an=6026-14x0=1 x 64 x 1=64

n1an-1 b=6125-14x1=6 x 32 x-14= -48x

n2an-2b2=6224-14x2=15×16 x116x2=15x2

n3an-3b3=6323-14x3=20 x 8 x-14x3=52x3

2-14x6=64-48x+15x2-52x3+...

b-​​ 

2-14x6+ 2+14x6=64-48x+15 x2-52x3++4-48x+15 x2-52x3+

=64-48x+15x2-52x3+64+48x+15x2+52x3

=128+30x2

Hence,​​ 

a=128

b=30