Question

How do you expand `(t+2)^6`?

Answer 1

`:.(t+2)^6 = t^6+12t^5+60t^4+160t^3+240t^2+192t+64`

Explanation:

We know `(a+b)^n= nC_0 a^n*b^0 +nC_1 a^(n-1)*b^1 + nC_2 a^(n-2)*b^2+..........+nC_n a^(n-n)*b^n`

Here `a=t,b=2,n=6` We know, `nC_r = (n!)/(r!*(n-r)!`
`:.6C_0 =1 , 6C_1 =6, 6C_2 =15,6C_3 =20, 6C_4 =15,6C_5 =6,6C_6 =1`

`:.(t+2)^6 = t^6+6*t^5*2+15*t^4*2^2+20*t^3*2^3+15*t^2*2^4+6*t*2^5+2^6` or

`:.(t+2)^6 = t^6+12*t^5+60*t^4+160*t^3+240*t^2+192*t+64` or

`:.(t+2)^6 = t^6+12t^5+60t^4+160t^3+240t^2+192t+64` [Ans]