Question

A expressão algébrica que representa o desenvolvimento do binômio (x+a)⁶é?
a)x⁶+6x⁵a+15x⁴a²+20x³a³+15x²a⁴+6xa⁵+a⁶
b)x⁶+7x⁵a+15x⁴a²+20x³a³+15x²a⁴+7xa⁴+a⁶
c)x⁶+6x⁵a+15x⁴a²+20x³+a³+15x²a⁴+7xa⁴
d)x⁶+7x⁵a+15x⁴a³+15x²a⁴+7xa⁴+a⁶

Answer 1

   $(x+a)^{6}=$

$=C_0^6x^{6}a^{0}+C_1^6x^{5}a^{1}+C_2^6x^{4}a^{2}+C_3^6x^{3}a^{3}+C_4^6x^{2}a^{4}+C_5^6x^{1}a^{5}+C_6^6x^{0}a^{6}=$

$=1x^{6}*1+6x^{5}a+15x^{4}a^{2}+20x^{3}a^{3}+15x^{2}a^{4}+6xa^{5}+1*1a^{6}=$

$=x^{6}+6x^{5}a+15x^{4}a^{2}+20x^{3}a^{3}+15x^{2}a^{4}+6xa^{5}+a^{6}$

Resposta: a)