Question

25a^2c^2+20acd+4d^2 trinomio cuadrado perfecto ​

Answer 1

Respuesta:

Explicación paso a paso:

$\mathfrak{Recordemos}\,\mathfrak{que}\,\mathfrak{un}\,\mathfrak{trinomio}\,\mathfrak{cuadrado}\,\mathfrak{perfecto}\\\mathfrak{se}\,\mathfrak{expresa}\,\mathfrak{como:}\\\\\mathfrak{a^{2}+2ab+b^{2}}=\mathfrak{(a+b)^{2}}\\\mathfrak{a^{2}-2ab+b^{2}}=\mathfrak{(a-b)^{2}}\\\textbf{Por lo tanto aplicando la primera con}\,\,a^{2}=25a^{2}c^{2}\,\,b^{2}=4d^{2}\,\,2ab=20acd\,\textbf{ nos queda:}\\\\25a^{2}c^{2}+20acd+4d^{2}\\a=\sqrt{25a^{2}c^{2}}=5ac\\b=\sqrt{4d^{2}}=2d\\2ab=(2)(5ac)(2d)=20acd\\\mathfrak{25a^{2}c^{2}+20acd+4d^{2}}=\mathfrak{(5ac+2d)^{2}}\\\textbf{As\'i concluimos que:}\\\\25a^{2}c^{2}+20acd+4d^{2}=(5ac+2d)^{2}$