# Thread: Binomail theorem

1. ## Binomail theorem

use the binomial theorem to expand and simplify the expression.

(a-3b)^5

can someone please explain to me how to use pascal"s triangle? i dont understand how they can just pull a bunch of numbers out of there?

2. Originally Posted by flexus
use the binomial theorem to expand and simplify the expression.

(a-3b)^5

can someone please explain to me how to use pascal"s triangle? i dont understand how they can just pull a bunch of numbers out of there?
the coefficients of the expanded form of $(x+y)^5$ are contained in the 6th row of Pascal's triangle ...

1 , 5 , 10 , 10 , 5 , 1

$(x+y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5
$

note that the exponents of $x$ start at 5 and decrease to 0 ... and the exponents of $y$ start at 0 and increase to 5.

now, replace $x$ with $a$ and $y$ with $(-3b)$

$(a-3b)^5 = a^5 + 5a^4(-3b) + 10a^3(-3b)^2 ...$ and so on

3. Originally Posted by skeeter
the coefficients of the expanded form of $(x+y)^5$ are contained in the 6th row of Pascal's triangle ...

1 , 5 , 10 , 10 , 5 , 1

$(x+y)^5 = x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5
$

note that the exponents of $x$ start at 5 and decrease to 0 ... and the exponents of $y$ start at 0 and increase to 5.

now, replace $x$ with $a$ and $y$ with $(-3b)$

$(a-3b)^5 = a^5 + 5a^4(-3b) + 10a^3(-3b)^2 ...$ and so on
thank you so much for taking you rtime to help me skeeter. but i don't see how you knew to use those numbers? is there anyway you could explain a little more deep. im sorry to ask so much. just don't understand this stuff. when i look at it all i see is a dark forest lol.