C2 expansion and coefficient help

Find and simplify the first four terms in the expansion of (1 + 4x)7 in ascending powers of x. [4]

Ive expanded this to be 1 + 28x + 336x sq + 2240x cubed and its correct

(ii) In the expansion of
(3 + ax)(1 + 4x)7,
the coefficient of x2 is 1001. Find the value of a.

However, I've looked in my textbook and I have no idea where to start or what to do. If someone could help I'd really appreciate it.

OP

bump

times through the two brackets for all the terms that will give you an x^2 then make this coef. including a = 1001 and solve to find a

start with
(3 + ax) (1 + 28x + 336x^2 + 2240x^3)
so if you mulptiply only the terms that will give an x^2 you get

1008x^2 + 28ax^2

so 1008 + 28a = 1001
28a = -7
a = -7/28

^ if thats not right then sorry I'm tired lol

Reply 3

peachesandcream77

OP

1

Original post by tgarrud

times through the two brackets for all the terms that will give you an x^2 then make this coef. including a = 1001 and solve to find a

start with
(3 + ax) (1 + 28x + 336x^2 + 2240x^3)
so if you mulptiply only the terms that will give an x^2 you get

1008x^2 + 28ax^2

so 1008 + 28a = 1001
28a = -7
a = -7/28

^ if thats not right then sorry I'm tired lol

Oooooh! I get it now. Thank you so much.

Reply 4

wasting-time

9

no probs. I have C2 tomorrow haha

Reply 5

peachesandcream77

OP

1

Verify x = 2 is a root of the equation

(2x+5)^4 - (2x-5)^4 = 3680x - 800 and find all other possible values of x

I got the expansion of (2x+5)^4 if that helps as

16x^4 + 160x3 + 600x2 + 1000x + 625

If someone could point me in the right direction then i would be really grateful, really stuck on this question.

OP

bump

EXPAND the photo

I use long division

Original post by peachesandcream77

Verify x = 2 is a root of the equation

(2x+5)^4 - (2x-5)^4 = 3680x - 800 and find all other possible values of x

I got the expansion of (2x+5)^4 if that helps as

16x^4 + 160x3 + 600x2 + 1000x + 625

If someone could point me in the right direction then i would be really grateful, really stuck on this question.

You substitute x=2 into each side and they should be the same. I remember seeing this before.
I think I moved the 360x -800 to the left and showed that it equals zero, but there is no need to.

Oh and afterwards you will find that when you expand the LHS that every other term eliminate because of the (-) in front of the five, you should be left with a simpler polynomial to solve.

It is the Jan 08 paper right? I've just found my answer.

(edited 12 years ago)

C2 expansion and coefficient help

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