Question

what is formula of (a+b) whole power 7

Answer 1

Heya User,

--> Using Binomial Expansion:->

---> $[ a + b ]^7$$=a^7+^7C_1a^6b+^7C_2a^5b^2 +^7C_3a^4b^3+^7C_4a^3b^4+^7C_5a^2b^5+^7C_6ab^6+b^7$

Hence, putting the values of Co-efficients respectively:->

$[a+b]^7 = a^7 + 7a^6b + 21a^5b^2 + 35a^4b^3 + 35a^3b^4 + 21a^2b^5 + 7ab^6 +b^7$

Here you go with your --> expansion!!

Answer 2

Answer:

$a^7 + 7 a^6 b + 21 a^5 b^2 + 35 a^4 b^3 + 35 a^3 b^4 + 21 a^2 b^5 + 7 a b^6 + b^7$

Step-by-step explanation:

The given expression is

$(a+b)^7$

The binomial expansion:

$(a+b)^n=^nC_0a^n+^nC_1a^{n-1}b+...+^nC_{n-1}a^1b^{n-1}+^nC_{n}b^n$

The binomial expansion of given expression is

$(a+b)^7=^7C_0a^7+^7C_1a^{6}b+^7C_{2}a^{7-2}b^{2}+^7C_{3}a^{7-3}b^{3}+^7C_{4}a^{7-4}b^{4}+^7C_{5}a^{7-5}b^{5}+^7C_{6}a^{7-6}b^{6}+^7C_{7}b^7$

$^nC_r=\frac{n!}{r!(n-r)!}$

$(a+b)^7=a^7+7a^{6}b+21a^{5}b^{2}+35a^{4}b^{3}+35a^{3}b^{4}+21a^{2}b^{5}+7a^1b^{6}+b^7$

Therefore, the formula for $(a+b)^7$ is

$a^7 + 7 a^6 b + 21 a^5 b^2 + 35 a^4 b^3 + 35 a^3 b^4 + 21 a^2 b^5 + 7 a b^6 + b^7$