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Practice Badges Formatting Help Simplify. (-5)*(a-2b+3c-4d)-(-3)*(4a-3b+2c-d)

Practice\newlineBadges\newlineFormatting Help\newlineSimplify.\newline(−5)⋅(a−2b+3c−4d)−(−3)⋅(4a−3b+2c−d) (-5) \cdot(a-2 b+3 c-4 d)-(-3) \cdot(4 a-3 b+2 c-d)

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Q. Practice\newlineBadges\newlineFormatting Help\newlineSimplify.\newline(−5)⋅(a−2b+3c−4d)−(−3)⋅(4a−3b+2c−d) (-5) \cdot(a-2 b+3 c-4 d)-(-3) \cdot(4 a-3 b+2 c-d)
  1. Distribute −5-5: Distribute −5-5 through (a−2b+3c−4d)(a-2b+3c-4d).\newlineCalculation: −5a+10b−15c+20d-5a + 10b - 15c + 20d
  2. Distribute −3-3: Distribute −3-3 through (−1)⋅(4a−3b+2c−d)(-1)\cdot(4a-3b+2c-d).\newlineCalculation: 12a−9b+6c−3d12a - 9b + 6c - 3d
  3. Add Distributions: Add the results of the two distributions.\newlineCalculation: (−5a+10b−15c+20d)+(12a−9b+6c−3d)(-5a + 10b - 15c + 20d) + (12a - 9b + 6c - 3d)\newline=(−5a+12a)+(10b−9b)+(−15c+6c)+(20d−3d)= (-5a + 12a) + (10b - 9b) + (-15c + 6c) + (20d - 3d)\newline=7a+b−9c+17d= 7a + b - 9c + 17d

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