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- WE WANT TO COMBINE THE LIKE TERMS
IN THE EXPRESSIONS.
BUT BEFORE WE COMBINE LIKE TERMS,
WE DO HAVE TO ELIMINATE THE PARENTHESES BY DISTRIBUTING.
SO IN THIS FIRST EXAMPLE, WE HAVE TO DISTRIBUTE 3.
SO WE'LL HAVE 3 x X - 3 x 4, SO THAT WOULD BE 3X - 12
AND WE HAVE - 4X + 5.
NOW, LET'S IDENTIFY THE LIKE TERMS.
THE 1st TERM AND THE 3rd TERM HAVE EXACTLY 1 FACTOR OF X,
AND THEREFORE THOSE ARE LIKE TERMS.
AND THEN THE 2nd AND 4th TERMS ARE ALSO LIKE TERMS
BECAUSE THEY'RE CONSTANTS.
AND THEN 3X - 4X WOULD BE -1X.
THE VARIABLE PART STAYS THE SAME,
AND THEN WE SUBTRACT THE COEFFICIENTS AND 3 - 4
IS EQUAL TO -1.
AND THEN TO COMBINE THE CONSTANTS,
REMEMBER WE CAN THINK OF THIS AS + -12.
SO WE'LL HAVE -12 + 5 WHICH WOULD BE -7,
SO WE CAN PUT + -7.
BUT WE DON'T WANT TO LEAVE OUR EXPRESSION
IN THIS FORM.
-1 x X WOULD JUST BE -X. AND THEN INSTEAD OF ADDING -7,
WE CAN SUBTRACT +7.
SO THIS IS THE FORM WE WANT OUR EXPRESSION
TO BE IN AFTER COMBINING LIKE TERMS.
IN THE 2nd EXPRESSION, WE HAVE TO DISTRIBUTE HERE
AND HERE BEFORE WE COMBINE LIKE TERMS.
SO 4 x 3Y WOULD BE 12Y - 4 x 1 IS 4.
NOW BECAUSE WE HAVE A MINUS SIGN HERE,
WE DO HAVE TO BE CAREFUL.
WE'LL HAVE - 5 x 2Y, THAT'S 10Y, AND THEN - 5 x 4
WOULD BE 20.
SO WE'RE SUBTRACTING BOTH OF THESE PRODUCTS,
AND NOW 12Y AND 10Y ARE LIKE TERMS.
AND THEN THE CONSTANTS ARE LIKE TERMS AS WELL,
SO 12Y - 10Y WOULD BE 2Y.
AND THEN TO COMBINE THE CONSTANTS,
WE CAN THINK OF THIS AS -4 - 20 WHICH WOULD BE -24.
BUT INSTEAD OF WRITING + -24, WE'RE GOING TO WRITE - +24.
OKAY. I HOPE YOU FOUND THESE EXAMPLES HELPFUL.