Given: " "color(brown)(color(green)(2/3)(6r+9s))color(blue)(+)color(magenta)(1/4)color(black)((8r+12s)) 23(6r+9s)+14(8r+12s)
color(blue)("What this is really saying?")What this is really saying?
" Everything inside of "color(brown)((6r+9s)) " is multiplied by "color(green)(2/3) Everything inside of (6r+9s) is multiplied by 23
" Everything inside of "(8r+12s) " is multiplied by "color(magenta)(1/4) Everything inside of (8r+12s) is multiplied by 14
color(blue)("Lets apply this!")Lets apply this!
[(color(green)(2/3)xx color(brown)(6r))color(brown)(+)(color(green)(2/3)xxcolor(brown)(9s))] color(blue)(+)[(color(magenta)(1/4)xx8r)+(color(magenta)(1/4)xx12s)] [(23×6r)+(23×9s)]+[(14×8r)+(14×12s)]
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When multiplying you must be very careful about signs. Fore example: ""
(-1)xx(+1)=(-1) " and that " (-1)xx(-1)=(+1)(−1)×(+1)=(−1) and that (−1)×(−1)=(+1). In
""
this instance it is very straight forward in that everything is positive!
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=> 4r+6s+2r+3s⇒4r+6s+2r+3s
=>6r+9s⇒6r+9s