Identify Grouping Strategy: Step Title: Identify the Grouping StrategyConcise Step Description: Group terms in the expression to prepare for factoring by grouping.Step Calculation: Group the terms as 20tu−10t and 2u−1.Step Output: Grouped terms: 20tu−10t+2u−1
Factor Common Factors: Step Title: Factor Out the Common Factors in Each GroupConcise Step Description: Factor out the greatest common factor from each group.Step Calculation: From the first group 20tu−10t, factor out 10t. From the second group 2u−1, factor out 1.Step Output: Factored groups: 10t(u−1)+1(2u−1)
Identify Common Binomial: Step Title: Identify a Common BinomialConcise Step Description: Look for a common binomial factor between the two groups.Step Calculation: The common binomial factor is (u−1).Step Output: Common binomial factor: (u−1)
Factor by Grouping: Step Title: Factor by GroupingConcise Step Description: Write the expression as the product of the common binomial factor and the remaining terms.Step Calculation: The factored expression is (u−1)(10t+1).Step Output: Factored expression: (u−1)(10t+1)