Question

ao desenvolver o binomio (3x + 1)^12 podemos dizer que teremos quantos termos desenvolvidos nesse polinômio?

Answer 1

$(3x + 1) {}^{12} = (3x + 1) {}^{3} \times (3x + 1) {}^{3} \times (3x + 1) {}^{3} \times (3x + 1) {}^{3} = \\ \\ = (27x {}^{3} + 27x {}^{2} + 9x + 1) \times (27x {}^{3} + 27x {}^{2} + 9x + 1) \times (27x {}^{3} + 27x {}^{2} + 9x + 1) \times (27x {}^{3} + 27x {}^{2} + 9x + 1) = \\ \\ = (729x {}^{6} + 729x {}^{5} + 243x {}^{4} + 27x {}^{3} + 729x {}^{5} + 729x {}^{4} + 243x {}^{3} + 27x {}^{2} + 243x {}^{4} + 243x {}^{3} + 81x {}^{2} + 9x +27x {}^{3} + 27x {}^{2} + 9x + 1) (729x {}^{6} + 729x {}^{5} + 243x {}^{4} + 27x {}^{3} + 729x {}^{5} + 729x {}^{4} + 243x {}^{3} + 27x {}^{2} + 243x {}^{4} + 243x {}^{3} + 81x {}^{2} + 9x +27x {}^{3} + 27x {}^{2} + 9x + 1)$