Cuanto es (x + y + 1)2 y cuánto es ( 2x + y + 3)2?

Buenas, vamos a resolver ambos trinomios cuadrados, mediante la demostración de trinomio al cuadrado.

DEMOSTRACIÓN de TRINOMIO AL CUADRADO :

<img src="https://tex.z-dn.net/?f=%28a%2Bb%2Bc%29%5E%7B2%7D%20%5C%5C%20%20%5C%5C%20a%2Bb%3Dx%20%5C%5C%20%20%5C%5C%20%28a%2Bb%2Bc%29%5E%7B2%7D%20%3D%28x%2Bc%29%5E%7B2%7D%20%5C%5C%20%20%5C%5C%20%28x%2Bc%29%5E%7B2%7D%3D%20x%5E%7B2%7D%20%2Bc%5E%7B2%7D%2B2xc%20%3D%28a%2Bb%29%5E%7B2%7D%2Bc%5E%7B2%7D%2B2%28a%2Bb%29c%20%5C%5C%20%20%5C%5C%20%28a%2Bb%29%5E%7B2%7D%2Bc%5E%7B2%7D%2B2%28a%2Bb%29c%20%20%5C%5C%20%20%5C%5C%20a%5E%7B2%7D%2Bb%5E%7B2%7D%2B2ab%2Bc%5E%7B2%7D%2B2%28a%2Bb%29c%20%5C%5C%20%20%5C%5C%20a%5E%7B2%7D%2Bb%5E%7B2%7D%2Bc%5E%7B2%7D%2B%202ab%20%2B2%28a%2Bb%29c%20%5C%5C%20%20%5C%5C%20a%5E%7B2%7D%2Bb%5E%7B2%7D%2Bc%5E%7B2%7D%2B%202ab%20%2B2ac%2B2bc%20%20%5C%5C%20%20%5C%5C%20a%5E%7B2%7D%2Bb%5E%7B2%7D%2Bc%5E%7B2%7D%2B2%28ab%2Bac%2Bbc%29" />

Ahora a reemplazar.

<img src="https://tex.z-dn.net/?f=%28x%2By%2B1%29%5E%7B2%7D%3Dx%5E%7B2%7D%2By%5E%7B2%7D%2B1%5E%7B2%7D%2B2%28xy%2Bx%281%29%2By%281%29%29%20%5C%5C%20%20%5C%5C%20x%5E%7B2%7D%2By%5E%7B2%7D%2B1%2B2%28xy%2Bx%2By%29" />

<img src="https://tex.z-dn.net/?f=%282x%2By%2B3%29%5E%7B2%7D%3D%282x%29%5E%7B2%7D%2By%5E%7B2%7D%2B3%5E%7B2%7D%2B2%282x%28y%29%2B2x%283%29%2By%283%29%29%20%5C%5C%20%20%5C%5C%20%204x%5E%7B2%7D%20%2By%5E%7B2%7D%2B9%2B2%282xy%2B6x%2B3y%29" />

Espero haberte ayudado ; ).