First three terms of this? How to do?...?

Question

Find the first three terms in the expansion of

(i) (3 + x) ^5

Please show your workings clearly. Thank you. =)

Answer 1

you must use this;

(x+y)^n => t(k+1) = nCk x^(n-k)y^(k) [think of k as a 'k'ounter]

then (5C0) 3^5(x)^0 + (5C1) 3^4(x)^1 + (5C2) 3^3(x)^2. . .

=> 3^5 + 5 (3^4)x + 10 (3^3)x^2 . . .
=> 243 + 405x + 270x^2. . .

sorry for the messiness but that's the best notation i could use for n 'choose' k.

Answer 2

(x+3)^5
x^5 x^4 x^3 x^2 x^1 x^0
5^0 5^1 5^2 5^3 5^4 5^5
3^5 3^4 3^3 3^2 3^1 3^0

243x^5+405x^4+3375x^3

+1125x^2+1875x+3125

Answer 3

Hello,

We have 5C0*3^5*X^0 + 5C1*3^4*X + 5C2*3^3*X =

243 + 405X + 270X^2

Hope This Helps!!

Answer 4

(a+b)^n=a^n+nC1a^(n-1)b^1+nC2a^(n-2)b^2+ -----------

here it is 3^5+5*3^4 *x + [5(5-1)/2]*3^3 *x^2+--------