# 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

THESE EXAMPLES HELPFUL.