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Binomial Expansion Question - A Level Maths

Q2.

f(x)=(a+bx)(2-x/16)^9

(a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of
giving each term in its simplest form. I have ended up with the terms 512 -144x+18x^2. (correct)
(4)
, where a and b are constants
Given that the first two terms, in ascending powers of x, in the series expansion of f(x) are
128 and 36x,
(b) find the value of a,
(2)
(c) find the value of b.
(2)

(Total for question = 8 marks)

Apparently to find a, you must form the equation 512a = 128.
I did (a+bx)(512) + 128. I do not understand why you end up with 512a = 128 and not 512a +512bx = 128. Please explain the reasoning

(edited 4 months ago)

Reply 1

abuzztheuk

well nobody can really help you if we don't even know the thing you're expanding

Reply 2

rishoo1

Original post by abuzztheuk

well nobody can really help you if we don't even know the thing you're expanding

my bad hahah

Reply 3

abuzztheuk

well you're in luck, somehow you got given a 2018 AS maths paper question
[url=AS]https://www.thestudentroom.co.uk/showthread.php?t=5555582]AS Pure Maths May 2018 Question - The Student Room
this will probably help?

(edited 4 months ago)

Reply 4

rishoo1

Original post by abuzztheuk

well you're in luck, somehow you got given a 2018 AS maths paper question
[url=AS]https://www.thestudentroom.co.uk/showthread.php?t=5555582]AS Pure Maths May 2018 Question - The Student Room

this will probably help?
i saw the thread.. the steps t makes no sense..

Reply 5

mqb2766

Original post by rishoo1

i saw the thread.. the steps t makes no sense..

Youre multiplying two polynomials and equating to a third so
(a+bx)(2-x/16)^9 = 128 + 36x + ...
Subbing in the first few terms of the binomial gives
(a+bx) (512 -144x+18x^2 + ...) = 128 + 36x + ...
Expand the terms on the left and equate to the right, specifically the constant and linear coefficients.

Reply 6

rishoo1

Original post by mqb2766

but when i expand the constant i end uup with 512a +512bx = 128 when i should be ending up with 512a =128?

Reply 7

mqb2766

Original post by rishoo1

but when i expand the constant i end uup with 512a +512bx = 128 when i should be ending up with 512a =128?

If its multiplied by x its not a constant as x is a variable. So equate the constant terms to get a, then equate the linear coefficients (of x) to get b.
Two polynomials are equal (for all values of x) if all their coefficients are equal