Question

(3x/4+2y/5)(3x/4-2y/5) como resolver ?

Answer 1

(3x/4+2y/5)(3x/4-2y/5) 9x²/16 - 4y²/25

Answer 2

Olá, Graziele !

Observe que:

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

Neste caso, temos $a=\dfrac{3x}{4}$ e $b=\dfrac{2y}{5}$.

Assim:

$\left(\dfrac{3x}{4}+\dfrac{2y}{5}\right)\left(\dfrac{3x}{4}-\dfrac{2y}{5}\right)=\left(\dfrac{3x}{4}\right)^2-\left(\dfrac{2y}{5}\right)^2$.

Por outro lado, note que:

$\left(\dfrac{3x}{4}\right)^2=\dfrac{(3x)^2}{4^2}=\dfrac{9x^2}{16}$

$\left(\dfrac{2y}{5}\right)^2=\dfrac{(2y)^2}{5^2}=\dfrac{4y^2}{25}$.

Logo:

$\left(\dfrac{3x}{4}+\dfrac{2y}{5}\right)\left(\dfrac{3x}{4}-\dfrac{2y}{5}\right)=\boxed{\dfrac{9x^2}{16}-\dfrac{4y^2}{25}}$

Espero ter ajudado, até mais ^^