Concept:Factor by grouping: arrange the terms into two pairs, factor each pair separately, then take out the common binomial factor.Explanation:Start with the expression 2xy−6y+7x−21.Group the terms as (2xy−6y)+(7x−21).Factor the first group: 2xy−6y=2y(x−3).Factor the second group: 7x−21=7(x−3).So the expression becomes 2y(x−3)+7(x−3).Now (x−3) is common in both terms.Factor it out to get (x−3)(2y+7).This is the completely factorized form.Answer:(x−3)(2y+7), which is option A.