Question

Expand the binomial (a+2)^4

Answer 1

Explanation:

Answer 2

Answer:
`a^4+8a^3+24a^2+32a+16`

Explanation:

The binomial expansion of
`(a+b)^n=^nC_0a^nb^(0)+^nC_1a^(n-1)b^1+^nC_2a^(n-2)b^2+.........+^nC_na^0b^n`

For
`(a+2)^4` , n=4 and b= 2 , we have

Then, the binomial expansion of
`(a+2)^4` will be :

`(a+2)^4=^4C_0a^4(2)^(0)+^4C_1a^(4-1)2^1+^4C_2a^(4-2)2^2++^4C_3a^(4-3)2^3++^4C_4a^(0)2^4\\\\=(1)a^4+(4)a^3(2)+(4!)/(2!(4-2)!)a^2(4)+(4)a(8)+(1)(16)`

∵
`^nC_0=^nC_n=0` and
`^nC_1=^nC_(n-1)=n`

`=a^4+8a^3+(6)a^2(4)+32a+16\\\\=a^4+8a^3+24a^2+32a+16`

Hence, the binomial expansion of
`(a+2)^4=a^4+8a^3+24a^2+32a+16`