Question

(3/4x + 2/5y)² produtos notáveis

Answer 1

AE manoo,

use a regra básica do quadrado da soma..

$(a+b)^2=a^2+2ab+b^2$

onde,

$\begin{cases}a= \dfrac{3}{4}x\\\\ b= \dfrac{2}{5}y \end{cases}$

_____________


$\left( \dfrac{3}{4}x+ \dfrac{2}{5}y\right)^2=\left( \dfrac{3}{4}x\right)^2+2\cdot \dfrac{3}{4}x\cdot \dfrac{2}{5}y+\left( \dfrac{2}{5}y\right)^2\\\\\\ \left( \dfrac{3}{4}x+ \dfrac{2}{5}y\right)^2= \dfrac{9}{16}x^2+ \dfrac{12}{20}xy+ \dfrac{4}{25}y^2~~(simplifica~por~4,~o~ \dfrac{12}{20}xy ) \\\\\\ \Large\boxed{\left( \dfrac{3}{4}x+ \dfrac{2}{5}y\right)^2= \dfrac{9}{16}x^2+ \dfrac{3}{5}xy+ \dfrac{4}{25}y^2}$

Answer 2

Produto Notável ---> O quadrado do 1° mais duas vezes o 1° multiplicado pelo 2° mais o quadrado do 2°.


$\left( \dfrac{3x}{4} + \dfrac{2y}{5} \right)^2\to \\\\\\ \left( \dfrac{3x}{4} + \dfrac{2y}{5} \right) . \left( \dfrac{3x}{4} + \dfrac{2y}{5} \right)\to \\\\\\ \left( \dfrac{3x}{4} .\dfrac{3x}{4} \right) +\left( \dfrac{3x}{4}. \dfrac{2y}{5} \right)+\left( \dfrac{2y}{5}.\dfrac{3x}{4} \right) +\left( \dfrac{2y}{5}.\dfrac{2y}{5} \right) \to\\\\\\ \dfrac{9x^2}{16} + \dfrac{6xy}{20} + \dfrac{6xy}{20} + \dfrac{4y^2}{25} \to$



$\dfrac{9x^2}{16} +2\left( \dfrac{6xy}{20} \right) + \dfrac{4y^2}{25} \to \\\\\\ \dfrac{9x^2}{16} + \dfrac{12xy}{20} + \dfrac{4y^2}{25}\to \\\\ \\ \Large\boxed{\boxed{ \dfrac{9x^2}{16} + \dfrac{3xy}{5} + \dfrac{4y^2}{25} }}$