Разложите на множители: а) ax+ay-x^2-2xy-y^2 б) a^2-2ab+b^2-a+b в) a^2-b^2-c^2+2bc

а) a*x + a*y - x^2 - 2*x*y - y^2 = a*x + a*y - (x^2 + 2*x*y + y^2 ) = a*(x + y) - (x^2 + 2*x*y + y^2 ) = a*(x + y) - (x + y)^2 = (x + y)*(a - (x + y)) = (x + y)*(a - x - y).б) a^2 - 2*a*b + b^2 - a + b = a^2 - 2*a*b + b^2 - (a - b) = (a - b)^2 - (a - b) = (a - b)*(a - b - 1).в) a^2 - b^2 - c^2 + 2*b*c = a^2 - (b^2 + c^2 - 2*b*c) = a^2 - (b^2 - 2*b*c + c^2) = a^2 - (b - c)^2 = (a - (b - c))*(a + (b - c)) = (a - b + c)*(a + b - c).