
Hi, can anyone help with this binomial question please? Thank you
Hi, can anyone help with this binomial question please? Thank you
(2a+x)(1-3x)n = 4 -59x + bx2 + …..
Using the Binomial expansion of:
(1+x)n = 1 + nx + n!/[(n-2)! 2! ] x2 + ……… replacing x with (-3x)
(2a+x) { 1 + n(-3x) + n!/[(n-2)! 2! ] (-3x)2 + ……..} = 4 -59x + bx2 + …..
2a –(6an)x + n!/[(n-2)! 2! ](2a)(9x2) + (1) x – (3n) x2 + ……. = 4 –59x + bx2 + …….
2a = 4 => a = 2
Comparing coefficient of x and substituting a =2,
6an – 1 = 59 => 12n = 60 => n = 5
Comparing coefficient of x2 and substituting n = 5, a =2,
b = (5!/2!3!) (18×2) – 15 = 360 – 15 = 345
Therefore, a = 2, n = 5 and b = 345
Please click “Accept Answer” if the answer is correct.