– WE WANT TO USE

THE DISTRIBUTIVE PROPERTY TO SIMPLIFY

THE GIVEN EXPRESSIONS. SO, HERE WE HAVE

5 x THE QUANTITY X + 2. SO, WE NEED TO MULTIPLY

THE 5 AND THE X AS WELL AS THE 5 AND THE 2,

AND SOMETIMES YOU’LL HEAR DISTRIBUTION REFERRED TO

AS MULTIPLICATION ACROSS ADDITION OR SUBTRACTION,

AND THIS IS WHY. SO, WE’LL HAVE 5 x X + 5 x 2. WELL, 5 x X WOULD BE 5X,

AND 5 x 2=10. SO, WE HAVE 5X + 10. IN THE SECOND EXAMPLE

WE’RE DISTRIBUTING +3. SO WE’LL HAVE +3 x X – +3 x 9. SO WE’LL HAVE 3 x X – 3 x 9. WELL, 3 x X=3X – 3 x 9=27. LET’S GO AND TAKE A LOOK

AT TWO MORE EXAMPLES. HERE WE HAVE

2 x THE QUANTITY 3Y + 7. SO WE’LL DISTRIBUTE THE 2.

SO WE’LL HAVE 2 x 3Y + 2 x 7. WELL, 2 x 3Y WOULD BE 6Y AND 2 x 7=14. SO WE HAVE 6Y + 14. AND FOR THE LAST EXAMPLE,

WE HAVE -3 x THE QUANTITY N – 4. SO WE’RE DISTRIBUTING -3. SO WE’LL HAVE -3 x N – (-3) x 4. AND WE NEED TO BE A LITTLE

CAREFUL WHEN DISTRIBUTING A NEGATIVE

AND WE HAVE SUBTRACTION. SO WE’LL HAVE -3 x N – (-3) x 4. SO -3 x N IS -3N.

AND HERE WE HAVE TO BE CAREFUL. WE’RE GOING TO HAVE – (-3) X 4,

WHICH WOULD BE – (-12), BUT REMEMBER

SUBTRACTING A NEGATIVE IS THE SAME

AS ADDING A POSITIVE. SO THIS BECOMES + (+12). SO WE SHOULD BE

A LITTLE EXTRA CAREFUL WHEN DISTRIBUTING A NEGATIVE,

AND WE HAVE SUBTRACTION. ANOTHER WAY TO REMEMBER THIS IS

AS + 12, WE CAN THINK OF THIS AS -3 x -4,

WHICH WOULD BE A +12.