Simplify: a²(a−b + c) + b²(a + b−c)−c²(a−b−c)

Here we have the polynomials as a²(a−b + c), b²(a + b−c) and c²(a−b−c)

Now using the distributive law, a²(a−b + c) = a²(a)-a²(b) + a²(c) = a³-a²b + a²c

b²(a + b−c) = b²(a) + b²(b)-b²(c) = ab² + b³-b²c and c²(a−b−c) = c²a-c²b-c³

Now we will simplify it, a²(a−b + c) + b²(a + b−c)−c²(a−b−c) = (a³-a²b + a²c) + (ab² + b³-b²c)-(c²a-c²b-c³) = a³-a²b + a²c + ab² + b³-b²c-c²a + c²b + c³ = a³ + b³ + c³-a²b + a²c + ab²-b²c-c²a + c²b

Hence , a²(a−b + c) + b²(a + b−c)−c²(a−b−c) = a²b + a²c + ab²-b²c-c²a + c²b