# Simple Binomial Expansion

• Mar 7th 2009, 09:27 AM
db5vry
Simple Binomial Expansion
This is a two part question: First it asks to expand $\displaystyle (a + b)^5$, and then to find the coefficient of $\displaystyle x^3$ in the expansion of $\displaystyle (1/4 + 2x)^5$.

I know for part one, you get $\displaystyle a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5$, and that somehow the values of the following are substituted in this answer, but I am not really sure on how this is done or written. Could someone please help in this?
• Mar 7th 2009, 09:36 AM
JeWiSh
Quote:

Originally Posted by db5vry
This is a two part question: First it asks to expand $\displaystyle (a + b)^5$, and then to find the coefficient of $\displaystyle x^3$ in the expansion of $\displaystyle (1/4 + 2x)^5$.

I know for part one, you get $\displaystyle a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5$, and that somehow the values of the following are substituted in this answer, but I am not really sure on how this is done or written. Could someone please help in this?

Well in the second expansion $\displaystyle a=\frac{1}{4}$ and $\displaystyle b=2x$

So, the coefficient of [/tex]x^3[/tex] is the $\displaystyle 10a^2b^3$ part of the expansion, just replace a and b with the values you have.
• Mar 7th 2009, 09:37 AM
Plato
You what the term $\displaystyle 10a^2 b^3$ where $\displaystyle a = \frac{1}{4}\;\& \;b = 2x$.
• Mar 7th 2009, 09:51 AM
db5vry
Quote:

Originally Posted by Plato
You what the term $\displaystyle 10a^2 b^3$ where $\displaystyle a = \frac{1}{4}\;\& \;b = 2x$.

So it is written as $\displaystyle 10(1/4)^2(2x)^3$, which is

$\displaystyle 10 x 1/16 x 8$
Which is also 10 multiplied by 0.5
Which is 5
Making the answer $\displaystyle 5x^3$?
• Mar 7th 2009, 09:53 AM
JeWiSh
Quote:

Originally Posted by db5vry
So it is written as $\displaystyle 10(1/4)^2(2x)^3$, which is

$\displaystyle 10 x 1/16 x 8$
Which is also 10 multiplied by 0.5
Which is 5
Making the answer $\displaystyle 5x^3$?

(Nod)
• Mar 7th 2009, 09:53 AM
db5vry
Quote:

Originally Posted by db5vry
So it is written as $\displaystyle 10(1/4)^2(2x)^3$, which is

$\displaystyle 10 x 1/16 x 8$
Which is also 10 multiplied by 0.5
Which is 5
Making the answer $\displaystyle 5x^3$?

Mis-use of Latex - That one line was 10 x 1/16 x 8.
Have I got the right answer?