Question

write the binomial expansion of (4x-3)^5
i really and lost on tis topic please explain cleary thanks

Answer 1

general form is
\[(a+b)^n=\sum_{k=0}^n\dbinom{n}{k}a^kb^{n-k}\]

Answer 2

here \(n=5, a=4x,b=-3\) so your but before we compute, lets find the fifth line of pascal's triangle. do you know how to do that?

Answer 3

i do no the triangle

Answer 4

the last line of the triangle pictured on the right is what you need
http://en.wikipedia.org/wiki/Pascal%27s_triangle

Answer 5

i do so the coefficients are 1,5,10,10,5,1

Answer 6

the last line is
1 5 10 10 5 1
so your expansion is going to look like
\[(4x)^5+5\times (4x)^4\times (-3)^1+10\times (4x)^3\times (-3)^2\]
\[+10\times (4x)^2\times (-3)^3+5\times (4x)^1\times (-3)^4+(-3)^5\]
yes and now you have a bunch of arithmetic to do to clean this up

Answer 7

wait wheres the variable
y

Answer 8

There is no variable y in your question...

Answer 9

no my teacher told me that u change (4x-3)^5 to (x+y)^5 to make it easier then

Answer 10

u just plug it in

Answer 11

but see thats were i get lost

Answer 12

Hmm...
in that case
x=4x, y=-3
That's what satellite73 has plugged in :|

Answer 13

Here it goes...
\[(x+y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 +5xy^4 + y^5\]
Put, x=4x and y=-3 into above expression.
\[(4x-3)^5 = (4x)^5 + 5(4x)^4(-3) + 10(4x)^3(-3)^2 \]\[+ 10(4x)^2(-3)^3 +5(4x)(-3)^4 + (-3)^5\]

Answer 14

okay so then do a add all of the 3s with the exponets

Answer 15

Then you should simplify the terms...
for example, (4x)^5 = 1024x^5 , 5(4x)^4(-3) = -3840x^4 and so on..

Answer 16

ohhhh okay so i can combine the coefficent with "Y"

Answer 17

What do you mean?

Answer 18

so let me solve it and ill type the answer and u can tell me if my work is rite k just hold on a sec.

Answer 19

iwhat i mean is i can muitply 4 and ^5

Answer 20

Hmm... 4^5 = 4x4x4x4x4 ...

Answer 21

1024x^5-768x^4+576x^3-432x^2+324x-243

Answer 22

is that rite

Answer 23

The first term and the last terms are correct. The rest are not

Answer 24

okay i see wat i did ring i didnt mulptiy the coffients with it lol

Answer 25

i got it now thanks

Answer 26

Welcome!~