Question

No binômio (x+y)8 calcule a soma dos coeficientes binomiais

Answer 1

Resposta:

Explicação passo a passo:

(x+y)⁸

Sc= (1+1)⁸ = (2)⁸ = 256 ✓

Answer 2

$\displaystyle \sf \underline{Sabemos \ que \ uma \ expans{\~a}o \ binomial\ {\'e} \ do \ tipo} : \\\\ (x+y)^n = \sum^n_{k=0}\cdot {n\choose k}\cdot x^{n-k} \cdot y^{k } \\\\\\ Logo : \\\\ (x+y)^8 = \sum^8_{k=0}\cdot {8\choose k}\cdot x^{8-k}\cdot y^k \\\\\\ \underline{A \ soma\ dos \ coeficientes} : \\\\\ \sf {8\choose 0}+{8\choose 1}+{8\choose 2}+...+{8\choose 8} = \ ? \\ \\\\\ \underline{E \ sabemos \ que \ pela \ propriedade\ da \ linha \ que} :$

$\displaystyle \sf {n\choose 0 }+{n\choose 1 }+{n\choose 2 }+{n\choose n-1 }+{n\choose n } = 2^n$

Portanto :

$\displaystyle \sf {8\choose 0}+{8\choose 1}+{8\choose 2}+...+{8\choose 8} =2^8 \\\\\\ {8\choose 0}+{8\choose 1}+{8\choose 2}+...+{8\choose 8} = {256 } \\\\\\ \huge\boxed{\sf Soma\ dos \ coeficientes\ = 256 } \checkmark$