Question 31: Simplify the following expressions: \((a−b+c)^2−(b−c)^2+2ab−2ac\)

\(\begin{array}{*{20}{l}} {{{\left( {a – b + c} \right)}^2} – {{\left( {b – c} \right) }^2} + 2ab – 2ac}\\ { = {a^2} + {b^2} + {c^2} – 2ab – 2bc + 2ac – \left( {{b^2} – 2.bc + {c^2}} \right) + 2ab – 2ac}\\ { = {a^2} + {b^2} + {c^2} – 2ab – 2bc + 2ac – {b^2} + 2bc – {c^2} + 2ab – 2ac}\\ { = {a^2}} \end{array}\)