# Ex 2: The Distributive Property

– HERE ARE SOME MORE EXAMPLES
OF USING THE DISTRIBUTIVE PROPERTY
TO SIMPLIFY EXPRESSIONS. IN THE FIRST EXAMPLE WE HAVE
-9P x THE QUANTITY P + 2. SO, WE WANT TO DISTRIBUTE -9P,
WHICH MEANS WE WANT TO MULTIPLY -9P AND P
AS WELL AS -9P AND 2. SO, WE’D HAVE -9P x P + -9 x 2. WELL, -9P x P
IS GOING TO BE -9P TO THE SECOND
OR -9P SQUARED, AND THEN WE’LL HAVE + (-18),
BUT INSTEAD OF LEAVING IT IN THIS FORM AS + AND -,
IT’S MORE COMMON TO WRITE THIS AS SUBTRACTING A POSITIVE. SO, THIS IS EQUIVALENT
TO -9P SQUARED – (+18). IN THE NEXT EXAMPLE WE HAVE
-3 x THE QUANTITY R + 2S – 4. SO, NOW, WE’LL BE DISTRIBUTING
-3 TO ALL THREE OF THESE TERMS IN THE PARENTHESES. SO, WE’LL HAVE
-3 x R + -3 x 2S – (-3) x 4. SO, AGAIN, WE’LL HAVE
-3 x R + -3 x 2S – (-3) x 4. SO, AS YOU CAN SEE, WE DO HAVE
TO BE A LITTLE MORE CAREFUL WHEN DISTRIBUTING A NEGATIVE. SO, HERE WE’LL HAVE -3R. NOW, HERE WE’RE GOING
TO HAVE + (-6S). WE’RE GOING TO WRITE – (+6S), AND THEN HERE
WE’LL HAVE – (-12), BUT INSTEAD OF WRITING – (-12), WE’LL WRITE + (+12). LET’S TAKE A LOOK
AT ONE MORE EXAMPLE. HERE WE HAVE
5B x THE QUANTITY 2A + 8B – 1. SO, NOTICE AGAIN, WE’LL HAVE
THREE PRODUCTS HERE, HERE AND HERE. SO WE’LL HAVE
5B x 2A + 5B x 8B – 5B x 1. SO, 5B x 2A WILL BE 10AB + 5B x 8B WOULD BE 40B SQUARED, AND WE’LL HAVE -5B x 1. SO, WE’LL JUST HAVE – 5B. OKAY. I HOPE YOU FOUND