# Ex 2: Combining Like Terms

– HERE ARE TWO MORE EXAMPLES OF COMBINING LIKE TERMS
GIVEN AN EXPRESSION. HERE WE HAVE X SQUARED Y
+ 3XY SQUARED + 4X SQUARED Y. REMEMBER LIKE TERMS HAVE TO HAVE
THE EXACT SAME VARIABLE PART WHICH MEANS THEY MUST CONTAIN
THE EXACT SAME VARIABLE FACTORS. SO ANALYZING THESE 3 TERMS
VERY CLOSELY, NOTICE ONLY THE 1st TERM
AND THE 3rd TERM ARE LIKE TERMS, BECAUSE THEY’RE THE ONLY 2 TERMS THAT CONTAIN 2 FACTORS
OF X AND 1 FACTOR OF Y. SO THESE ARE THE ONLY 2 TERMS
THAT WE CAN COMBINE. AND NOW WE KNOW THAT
TO COMBINE LIKE TERMS, WE ADD OR SUBTRACT
THE COEFFICIENTS OR THE NUMBERS IN FRONT
OF THE VARIABLES. WELL, X SQUARED Y DOESN’T APPEAR
TO HAVE A COEFFICIENT, BUT IT DOES. REMEMBER MULTIPLYING BY 1
DOESN’T CHANGE ANYTHING, SO WE CAN THINK OF THIS
AS 1X SQUARED Y. SO 1X SQUARED Y + 4X SQUARED Y
WOULD BE EQUAL TO 5X SQUARED Y, AND THEN WE STILL HAVE
THE + 3XY SQUARED. SO BE CAREFUL WITH PROBLEMS
LIKE THIS AND MAKE SURE THE TERMS HAVE
THE EXACT SAME VARIABLE FACTORS. FOR THE SECOND EXAMPLE,
WE HAVE -7M – 4 + 2M + 9. WELL, THE 1st TERM HAS 1 FACTOR
OF M AND SO DOES THE 3rd TERM, SO THOSE ARE LIKE TERMS. NOTICE THE 2nd TERM AND 4th TERM
ARE CONSTANTS AND CONSTANTS ARE ALSO
LIKE TERMS, SO WE CAN COMBINE THESE 2 TERMS
AS WELL. SO -7M + 2M WOULD BE -5M, BECAUSE LOOKING AT
THE COEFFICIENTS, -7 + 2 IS EQUAL TO -5, AND THE
VARIABLE PART STAYS THE SAME. AND THEN FOR -4 + 9, IF WE NEED TO WE CAN THINK
OF -4 AS + -4, AND SINCE -4 + 9 WOULD BE +5,
WE WOULD HAVE +5. SO THESE TWO EXAMPLES WERE
A LITTLE BIT MORE INVOLVED. WE’LL TAKE A LOOK AT TWO MORE
EXAMPLES IN THE NEXT VIDEO WHERE WE HAVE DISTRIBUTION AS
WELL AS COMBINING LIKE TERMS.