Question

Usando o teorema binomial, desenvolva: (3x +2)3

Answer 1

$(3x+2)^3=\\ =\binom{3}{0}.(3x)^3.2^0+\binom{3}{1}.(3x)^2.(2)^1+\binom{3}{2}.(3x)^1(2)^2+\binom{3}{3}.(3x)^0.(2)^3=\\\\ =1.27x^3.1+3.9x^2.2+3.3x.4+1.1.8=\\\\ =27x^3+54x^2+36x+8\\\\ Sabe-se \ que:\\\\ \binom{3}{0}=\frac{3!}{0!3!}=\frac{6}{1.6}=1\\\\ \binom{3}{1}=\frac{3!}{1!2!}=\frac{6}{1.2}=3$