Question

Calcule: [(x+y)² - (x²+y²)]²

Answer 1

Dada a propriedade (quadrado da soma):

$\mathsf{\left(a+b\right)^2=a^2+2ab+b^2}$

= = = = =

Logo:

$\mathsf{=\left[\left(x+y\right)^2-\left(x^2+y^2\right)\right]^2}\\\\\mathsf{=\left[\left(x^2+2xy+y^2\right)-\left(x^2+y^2\right)\right]^2}\\\\\mathsf{=\left(\diagup\!\!\!\!x^2+2xy+\diagup\!\!\!\!y^2-\diagup\!\!\!\!x^2-\diagup\!\!\!\!y^2\right)^2}\\\\\mathsf{=\left(2xy\right)^2}\\\\\mathsf{=2^2x^2y^2}\\\\\mathsf{=\boxed{\mathsf{4x^2y^2}}}\: \: \checkmark$