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X
- WE WANT TO COMBINE THE LIKE TERMS IN THE GIVEN EXPRESSIONS.
LIKE TERMS ARE TERMS THAT HAVE THE EXACT SAME VARIABLE FACTORS.
SO FOR EXAMPLE, WE HAVE 5X + 3X,
THESE BOTH CONTAIN 1 FACTOR OF X,
AND THEREFORE THEY ARE LIKE TERMS
WHICH MEANS THEY CAN BE ADDED OR SUBTRACTED.
AND THE WAY WE COMBINE LIKE TERMS
IS WE ADD OR SUBTRACT THE COEFFICIENTS
WHICH ARE THE NUMBERS IN FRONT OF THE VARIABLES.
SO A NICE WAY TO SHOW HOW THIS WORKS
IS TO USE THE DISTRIBUTIVE PROPERTY IN THE REVERSE ORDER.
WE COULD FACTOR OUT THE VARIABLE FACTOR OF X
LEAVING US WITH 5 + 3, AND NOW WE ADD THE COEFFICIENTS.
SO WE HAVE 5 + 3 WHICH IS 8, SO THIS SIMPLIFIES TO 8X.
LOOKING AT THE SECOND EXAMPLE, AGAIN,
THESE ARE ALL LIKE TERMS
BECAUSE THEIR VARIABLE PARTS ARE EXACTLY THE SAME
OR CONTAIN THE SAME VARIABLE FACTORS.
THESE ALL CONTAIN 1 FACTOR OF Y,
AND THEREFORE THEY'RE LIKE TERMS SO THEY CAN BE COMBINED
BY ADDING AND SUBTRACTING THE COEFFICIENTS.
SO WE'LL SHOW THIS USING THE DISTRIBUTIVE PROPERTY
ONE MORE TIME.
IF WE FACTOR OUT THE VARIABLE Y,
WE'D BE LEFT WITH -3 + 9 - 8 FROM THE COEFFICIENTS.
SO WE HAVE -3 + 9,
THAT'S +6 - 8 WOULD BE -2, AND -2 x Y WOULD BE -2Y.
AFTER DOING SEVERAL OF THESE EXAMPLES,
YOU'LL PROBABLY STOP SHOWING THIS STEP HERE
USING THE DISTRIBUTIVE PROPERTY
AND JUST ADD OR SUBTRACT THE COEFFICIENTS IN YOUR HEAD.
LET'S TAKE A LOOK AT TWO MORE EXAMPLES.
HERE WE HAVE 12N TO THE 3rd - 9N TO THE 3rd.
AND AGAIN, THESE ARE LIKE TERMS
BECAUSE THEY BOTH CONTAIN EXACTLY 3 FACTORS OF N
WHICH MEANS WE CAN COMBINE THESE LIKE TERMS
BY SUBTRACTING THE COEFFICIENTS.
AND SINCE 12 - 9 = 3, THIS SIMPLIFIES TO 3N TO THE 3rd.
NOTICE HOW THE VARIABLE PART
NEVER CHANGES WHEN ADDING OR SUBTRACTING LIKE TERMS.
AND THIS LAST EXAMPLE
JUST REMINDS US THAT WE DO HAVE TO BE CAREFUL,
BECAUSE THERE ARE ONLY 2 LIKE TERMS IN THIS EXPRESSION.
THE 1st TERM AND THE 3rd TERM CONTAIN 5 FACTORS OF R
AND THEREFORE ARE LIKE TERMS.
THIS TERM HERE ONLY CONTAINS 4 FACTORS OF R,
SO IT'S NOT A LIKE TERM.
SO WE CAN ONLY COMBINE THE 1st AND 3rd TERM HERE.
AND 15R TO THE 5th - 18R TO THE 5th
WOULD BE -3R TO THE 5th SINCE 15 - 18 IS -3,
AND THEN WE STILL HAVE TO INCLUDE -9R TO THE 4th.
WE'LL LOOK AT SOME MORE EXAMPLES IN THE NEXT VIDEO.