Question

PLEASE HELP!!!

Answer 1

How do I expand this expression using the binomial theorem? \[(x - 4b)\]

Answer 2

Sorry, wrong equation.\[(x - 4b)^3\]

Answer 3

I have no idea about this, I haven't learned it yet >.<

Answer 4

\[(a+b)^n = \left(\begin{matrix}n \\ k\end{matrix}\right) \sum_{k=0}^{n} a^{n-k} * b^k\]
\[\left(\begin{matrix}n \\ k\end{matrix}\right) = \frac{ n! }{ k! *(n-k)! }\]

Answer 5

Okay, I think that helps by giving me the binomial formula. Thanks anyways @Secret-Ninja .

Answer 6

So, this would meanb = 4b?

Answer 7

\[(x-4b)^3 = \left(\begin{matrix}3 \\ k = 0\end{matrix}\right) \sum_{k=0}^{3} x^{3-0} * (-4b)^0\]
\[(x-4b)^3 = \frac {3!}{0!* (3-0)!}x^3 * 1\]
\[(x-4b)^3 = 1*x^3 * 1\]

similarly find values for k = 1, 2, 3 and add them

Answer 8

b = -4b
as we are taking (a+b) formula

Answer 9

Okay. I apologize if I am a little slow at this... So, to continue we keep adding to k? or n?

Answer 10

put k = 1
then (n-k) = 2

Answer 11

So, I can just disregard the E sign? It doesn't serve any function other than to explain what's going on?

Answer 12

thats summation. It means adding all those terms from k =0 to k = 3

Answer 13

So how is this? \[[x ^{3-0} \times (-4b)^0] + [x^{3-1} \times (-4b)^1] + [x^{3-2} \times (-4b)^2] + [x^{3-3} \times (-4b)^3]\]

Answer 14

\[\left[ \frac{ 3! }{ 0! *(3-0)! }* x^{3-0} *(-4b)^0)\right] + \left[ \frac{ 3! }{ 1! *(3-1)! }* x^{3-1} *(-4b)^1)\right] + \left[ \frac{ 3! }{ 2! *(3-2)! }* x^{3-2} *(-4b)^2)\right] + \left[ \frac{ 3! }{ 3! *(3-3)! }* x^{3-3} *(-4b)^3)\right]\]

Answer 15

Got it. One more question: what do the exclamation marks mean?

Answer 16

Factorial
3! = 3*2*1 = 6

Answer 17

Wow. Okay, let me try this...

Answer 18

okkk

Answer 19

\[[1 \times x^3 \times 1] + [3 \times x \times (-4b)]\]

Answer 20

\[+ [3 \times x^2 \times (-4b)^2] + [0 \times x^3 \times (-4b)^3]\]

Answer 21

There.

Answer 22

Did I do anything wrong?

Answer 23

\[\left[ 1 * x^3 *1 \right]+ \left[ 3 * x^2 *(-4b) \right]\]
\[+\left[ 3 * x *(-4b)^2 \right] + \left[ 1 * 1 *(-4b)^3 \right]\]

Answer 24

Okay, that makes much more sense. Thank you for all your help.

Answer 25

anytime :)