Answer
$(b+c)^8 = b^8 + 8a^7b+ 28b^6c^2 + 56b^5c^3 + 70b^4c^4+56b^3c^5 +28b^2c^6 + 8bc^7 + c^8$
Work Step by Step
The binomial formula is as follows:
$(a+b)^n = a^n + n/1!* a^{n-1}*b^1 + n(n-1)/2!* a^{n-2}*b^2 + n(n-1)(n-2)/3!* a^{n-3}*b^3 + . . . + b^n$
$a=b$
$b=c$
$n=8$
$(b+c)^8 = b^8 + 8/1!* a^{8-1}*b^1 + 8(8-1)/2!* b^{8-2}*c^2 + 8(8-1)(8-2)/3!* b^{8-3}*c^3 + 8(8-1)(8-2)(8-3)/4!* b^{8-4}*c^4+8(8-1)(8-2)(8-3)(8-4)/5!* b^{8-5}*c^5 +8(8-1)(8-2)(8-3)(8-4)(8-5)/6!* b^{8-6}*c^6 + 8(8-1)(8-2)(8-3)(8-4)(8-5)(8-6)/7!* b^{8-7}*c^7 + 8(8-1)(8-2)(8-3)(8-4)(8-5)(8-6)(8-7)/8!* b^{8-8}*c^8$
$(b+c)^8 = b^8 + 8/1!* a^7*b^1 + 8(8-1)/2!* b^6*c^2 + 8(8-1)(8-2)/3!* b^5*c^3 + 8(8-1)(8-2)(8-3)/4!* b^4*c^4+8(8-1)(8-2)(8-3)(8-4)/5!* b^3*c^5 +8(8-1)(8-2)(8-3)(8-4)(8-5)/6!* b^2*c^6 + 8(8-1)(8-2)(8-3)(8-4)(8-5)(8-6)/7!* b*c^7 + 8(8-1)(8-2)(8-3)(8-4)(8-5)(8-6)(8-7)/8!*c^8$
$(b+c)^8 = b^8 + 8*a^7*b^1 + 8*7/2* b^6*c^2 + 8*7*6/6* b^5*c^3 + 8*7*6*5/24* b^4*c^4+8*7*6*5*4/120*b^3*c^5 +8*7*6*5*4*3/6*5*4*3*2*1* b^2*c^6 + 8*7*6*5*4*3*2/7*6*5*4*3*2*1*b*c^7 + 8*7*6*5*4*3*2*1/8!*c^8$
$(b+c)^8 = b^8 + 8*a^7*b^1 + 4*7* b^6*c^2 + 8*7*b^5*c^3 + 7*2*5*b^4*c^4+8*7*b^3*c^5 +4*7*b^2*c^6 + 8*b*c^7 + c^8$
$(b+c)^8 = b^8 + 8a^7b+ 28b^6c^2 + 56b^5c^3 + 70b^4c^4+56b^3c^5 +28b^2c^6 + 8bc^7 + c^8$
