Concept:Expand the algebraic expression by multiplying terms, then combine like terms to simplify.Explanation:First expand (a+2b−c)(b−c):(a+2b−c)(b−c)=ab+2b2−bc−ac−2bc+c2Combine the like terms from this expansion:ab+2b2−3bc−ac+c2Now add the remaining terms: (a−c)2b=2ab−2bc and b2.So the full expression becomes:ab+2b2−3bc−ac+c2+2ab−2bc+b2Group and combine like terms:ab+2ab=3ab2b2+b2=3b2−3bc−2bc=−5bcThe simplified expression is:3b2+c2+3ab−5bc−acAnswer:3b2+c2+3ab−5bc−acThis matches option D.