(−5)*(a−2b+3c−4d)−(−3)*(4a−3b+2c−d)
multiply sets of parentheses on each side of the minus sign first
multiply -5 by everything in parentheses on the left. multiply -3 by everything in parentheses on right
=[(-5*a)+(-5*-2b)+(-5*3c)+(-5*-4d)] -
[(-3*4a)+(-3*-3b)+(-3*2c)+(-3*-d)]
= (-5a+10b-15c+20d) - (-12a+9b-6c+3d)
switch all signs in second parentheses and remove parentheses to combine like terms
= -5a+10b-15c+20d + 12a-9b+6c-3d
combine like terms
= (-5a+12a)+(10b-9b)+(-15c+6c)+(20d-3d)
= 7a + b - 9c + 17d
ANSWER: 7a + b - 9c + 17d
Whew! Long one. Hope I didn't miss anything and this is correct! Hope it helps! :)
