Question

passo a passo de como expandir e simplificar (2x+3) 2

Answer 1

Olá.

$Expandindo:\\ Produto\hspace{5} notavel: (a+b)^2 = a^2+2ab+b^2\\\\ (2x+3)^2 = 4x^2+12x+9\\\\ Passo\hspace{10}a\hspace{10}passo:\\\\ (2x+3)(2x+3)\\\\ (2x.2x)+(3.2x)+(2x.3)+(3.3)\\\\ 4x^2+6x+6x+9\\\\ 4x^2+12x+9$

$Simplificando:\\ 4x^2+12x+9\\A\hspace{10} funcao\hspace{10} do\hspace{10} segundo\hspace{10} grau\hspace{10} pode\hspace{10} ser\hspace{10} escrita\hspace{10} na\hspace{10} forma:\\ a(x-x^{'})(x-x^{''})$

$a=4\\ b=12\\ c=9\\\\ x = \frac{-b+-\sqrt{\Delta}}{2a}\\\\ \Delta = b^2-4ac\\\\ \Delta = 12^2-4.4.9\\\\ \Delta = 144 - 144\\\\ \Delta = 0\\\\ x = \frac{-12+-\sqrt0}{2.4}\\\\ x^{'} = \frac{-12+0}{8} = \frac{-12}{8} = -\frac{3}{2}\\\\ x^{''} = \frac{12-0}{8} = \frac{-12}{8} = -\frac{3}{2}$

$a.(x-x^{'})(x-x^{''})\\\\ 4[x-(-\frac{3}{2})][x-(-\frac{3}{2})]\\\\ 4(x+\frac{3}{2})(x+\frac{3}{2})\\\\ (4x+6)(4x+6) \hspace{20} \ \textgreater \ divide\hspace{5}por\hspace{5}2\hspace{5}para\hspace{5}simplificar\\\\ (2x+3)(2x+3) = (2x+3)^2$

$Observacoes:\\\\ (4x+6)^2 = (2x+3)^2\\\\ Demonstrando:\\\\ (2x+3)^2 = 4x^2+12x+9\\\\ (4x+6)^2 = 16x^2+48x+36 \\ todos\hspace{5} os\hspace{5} coeficientes\hspace{5} sao\hspace{5} multiplos\hspace{5} de\hspace{5} 4\\\\ \frac{16x^2}{4}+\frac{48x^2}{4}+\frac{36}{4} = 4x^2+12x^2+9 = (2x+3)^2$

Espero ter ajudado. Se ficar dúvidas, põe nos comentários.