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Factor.\newline20tu10t+2u120tu - 10t + 2u - 1

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Q. Factor.\newline20tu10t+2u120tu - 10t + 2u - 1
  1. Identify Grouping Strategy: Step Title: Identify the Grouping Strategy\newlineConcise Step Description: Group terms in the expression to prepare for factoring by grouping.\newlineStep Calculation: Group the terms as 20tu10t20tu - 10t and 2u12u - 1.\newlineStep Output: Grouped terms: 20tu10t+2u120tu - 10t + 2u - 1
  2. Factor Common Factors: Step Title: Factor Out the Common Factors in Each Group\newlineConcise Step Description: Factor out the greatest common factor from each group.\newlineStep Calculation: From the first group 20tu10t20tu - 10t, factor out 10t10t. From the second group 2u12u - 1, factor out 11.\newlineStep Output: Factored groups: 10t(u1)+1(2u1)10t(u - 1) + 1(2u - 1)
  3. Identify Common Binomial: Step Title: Identify a Common Binomial\newlineConcise Step Description: Look for a common binomial factor between the two groups.\newlineStep Calculation: The common binomial factor is (u1)(u - 1).\newlineStep Output: Common binomial factor: (u1)(u - 1)
  4. Factor by Grouping: Step Title: Factor by Grouping\newlineConcise Step Description: Write the expression as the product of the common binomial factor and the remaining terms.\newlineStep Calculation: The factored expression is (u1)(10t+1)(u - 1)(10t + 1).\newlineStep Output: Factored expression: (u1)(10t+1)(u - 1)(10t + 1)