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Factor.\newline7m37m25m+57m^3 - 7m^2 - 5m + 5

Full solution

Q. Factor.\newline7m37m25m+57m^3 - 7m^2 - 5m + 5
  1. Identify common factors: Look for common factors in pairs of terms.\newlineWe can group the terms as follows: (7m37m2)(7m^3 - 7m^2) and (5m+5)(-5m + 5).
  2. Factor out first group: Factor out the common factor from the first group.\newlineThe common factor in the first group is 7m27m^2.\newline7m37m2=7m2(m1)7m^3 - 7m^2 = 7m^2(m - 1)
  3. Factor out second group: Factor out the common factor from the second group.\newlineThe common factor in the second group is -5").\(\newline\$-5m + 5 = -5(m - 1)\)
  4. Write factored expression: Write the expression with the factored groups.\(\newline\)We have:\(\newline\)\(7m^3 - 7m^2 - 5m + 5 = 7m^2(m - 1) - 5(m - 1)\)
  5. Factor out common binomial: Factor out the common binomial factor.\(\newline\)The common binomial factor is \((m - 1)\).\(\newline\)\(7m^2(m - 1) - 5(m - 1) = (m - 1)(7m^2 - 5)\)