SOLUTION: 12c - 8d - 15rc + 10rd Please help me Factor this by Grouping

Question 32626: 12c - 8d - 15rc + 10rd Please help me Factor this by Grouping
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
12c - 8d - 15rc + 10rd
12c - 8d + (10rd - 15rc)
factor out 5r from the terms in parenthesis
12c - 8d + 5r(2d - 3c)
4(3c - 2d) + 5r(2d - 3c)
this is
-4(2d - 3c) + 5r(2d - 3c)
factor out the 2d - 3c
(2d - 3c)(5r - 4)
check this by picking some values for r,c and d
r = 3
c = 1
d = 7
12(1) - 8(7) - 15(3)(1) +10(3)(7) =
12 - 56 - 45 + 210 = 121
now the factors
(2(7) - 3(1))*(5(3) -4) =
(14 - 3)(15 - 4) =
11 * 11 = 121
OK

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