Answer :

Here we have the polynomials as a^{2}(a−b + c), b^{2}(a + b−c) and c^{2}(a−b−c)

Now using the **distributive law**, a^{2}(a−b + c) = a^{2}(a)-a^{2}(b) + a^{2}(c) = a^{3}-a^{2}b + a^{2}c

b^{2}(a + b−c) = b^{2}(a) + b^{2}(b)-b^{2}(c) = ab^{2} + b^{3}-b^{2}c and c^{2}(a−b−c) = c^{2}a-c^{2}b-c^{3}

Now we will simplify it, a^{2}(a−b + c) + b^{2}(a + b−c)−c^{2}(a−b−c) = (a^{3}-a^{2}b + a^{2}c) + (ab^{2} + b^{3}-b^{2}c)-(c^{2}a-c^{2}b-c^{3}) = a^{3}-a^{2}b + a^{2}c + ab^{2} + b^{3}-b^{2}c-c^{2}a + c^{2}b + c^{3} = a^{3} + b^{3} + c^{3}-a^{2}b + a^{2}c + ab^{2}-b^{2}c-c^{2}a + c^{2}b

Hence , a^{2}(a−b + c) + b^{2}(a + b−c)−c^{2}(a−b−c) = a^{2}b + a^{2}c + ab^{2}-b^{2}c-c^{2}a + c^{2}b

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