Question

Qual é a forma reduzida da expressão algébrica:

$(\frac{2x+y}{2})^{2} - (\frac{2x-y}{2})^{2}$

Answer 1

$( \frac{2x+y}{2}) ^2-( \frac{2x-y}{2} )^2\\\\\\ ( \frac{2x+y}{2}) *( \frac{2x+y}{2})-( \frac{2x-y}{2} )*( \frac{2x-y}{2})\\\\ \frac{4 x^{2} +2xy+2xy+y^2}{4} -\frac{4 x^{2} -2xy-2xy+y^2}{4}\to \\\\ \frac{4 x^{2} +4xy+y^2}{4} -\frac{4 x^{2} -4xy+y^2}{4}\to \\\\ mmc=4\\\\( 4 x^{2} +4xy+y^2)-(4 x^{2} -4xy+y^2)\to \\\\ 4 x^{2} +4xy+y^2-4 x^{2} +4xy-y^2\to \\\\ 0 x^{2} +8xy-0y^2\to \\\\8xy$