(x+2y)² - (x+2y)(x-2y) + 2(x-2y)² + 4xy = x² + 4xy + 4y² - (x² - 4y²) + 2(x² - 4xy + 4y²) + 4xy = x² + 4xy + 4y² - x² + 4y² + 2x² - 8xy + 8y² + 4xy = 2x² + 16y² Korzystałem z wzorów: (a+b)² = a² + 2ab + b² (a-b)² = a² - 2ab + b² (a+b)(a-b) = a² - b² ---------------------------------------------------------------------------------------------------- Litterarum radices amarae sunt, fructus iucundiores Pozdrawiam :)
[latex](x+2y)^2 - (x+2y)(x-2y) + 2(x-2y)^2 + 4xy =\ =x^2 +2cdot xcdot 2y +(2y)^2 -[x^2-(2y)^2]+2[x^2-2cdot xcdot 2y+(2y)^2]+\ +4xy =\ =x^2+4xy + 4y^2 -(x^2-4y^2) + 2(x^2 - 4xy + 4y^2) + 4xy = \ =x^2 + 4xy + 4y^2 - x^2 + 4y^2 + 2x^2 - 8xy + 8y^2 + 4xy = \ =2x^2 + 16y^2[/latex]
