Question

Expand the binomial (a+2)^4

Answer 1

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

Step-by-step 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 :

$(a+2)^4=^4C_0a^4(2)^{0}+^4C_1a^{4-1}2^1+^4C_2a^{4-2}2^2++^4C_3a^{4-3}2^3++^4C_4a^{0}2^4\\\\=(1)a^4+(4)a^3(2)+\dfrac{4!}{2!(4-2)!}a^2(4)+(4)a(8)+(1)(16)$

∵ $^nC_0=^nC_n=0$ 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 $(a+2)^4=a^4+8a^3+24a^2+32a+16$

Answer 2

Answer:

Step-by-step explanation: