Binomial theorem D: (2 Viewers)

[fullonoob]

find the coefficient
(3+x)(1-x)^15 find the term in x^4

(2-5x+x^2)(1+x)^11 find the term in x^9


:jaw: help please + full working out

 

[bored of sc]

find the coefficient
(3+x)(1-x)^15 find the term in x^4

(2-5x+x^2)(1+x)^11 find the term in x^9


:jaw: help please + full working out

x⁰*x⁴ and x¹*x³ are the two cominations of x⁴ in respective order to the brackets...
1C0*3*x⁰*15C4*(1)¹¹(-x)⁴ + 1C1*3⁰*x*15C3*1¹²*(-x)³
= 4095x⁴ -455x⁴
= 3640x⁴
= 3640

I did this quick, it might be wrong.

 

[lyounamu]

x⁰*x⁴ and x¹*x³ are the two cominations of x⁴ in respective order to the brackets...
1C0*3*x⁰*15C4*(1)¹¹(-x)⁴ + 1C1*3⁰*x*15C3*1¹²*(-x)³
= 4095x⁴ -455x⁴
= 3640x⁴
= 3640

I did this quick, it might be wrong.

you are right.

2nd one:

possible combo
x^0 . x^9 ; x^1 . x^8 ; x^2 . x^7

so 2 . 11C9 . 1^2 . x^9 + -5x . 11C8 . 1^3 . x^8 + x^2 . 11C7 . 1^4 . x^7 = -385x^9

I did real quick..let me see if I am right.

 

[clintmyster]

just a quick question, you know for the binomials with n>6 or something do you guys tend to use combinations over pascals triangle?

 

[Timothy.Siu]

just a quick question, you know for the binomials with n>6 or something do you guys tend to use combinations over pascals triangle?

i never use pascals triangle, i just use the calculator

 

[lyounamu]

just a quick question, you know for the binomials with n>6 or something do you guys tend to use combinations over pascals triangle?

um, no.

Calculator is your best friend for this topic.

 

[Timothy.Siu]

its also good to know the theory behind it, the combinations that is.