Ex 1: Combining Like Terms

– 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 […]

Ex: Combine a Sum and Difference of Two Logarithms

TO DEMONSTRATE THE PROPERTIES OF LOGARITHMS, WE’RE ASKED TO WRITE THE SUM OF THESE TWO LOGS AS A SINGLE LOG AND THE DIFFERENCE OF THESE TWO LOGS AS A SINGLE LOG. SO BECAUSE WE’RE TRYING TO COMBINE THE SUM OF TWO LOGS HERE, WE’LL BE USING THE PRODUCT PROPERTY OF LOGARITHMS GIVEN HERE, WHERE LOG […]

Identify Like Terms and Combine Like

In this lesson we will review how to identify like terms and also how to combine like terms to simplify a polynomial. Two or more terms are like terms if they have the same variable or variables with the same exponent. Another way to think of this is like terms have the exact same variable […]

Ex 3: Combining Like Terms Requiring Distribution

– 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 […]

Ex: Related Rates – Volume of a Melting Snowball

– A SPHERICAL SNOWBALL IS MELTING IN SUCH A WAY THAT ITS DIAMETER IS DECREASING AT A RATE OF 0.3 CENTIMETERS PER MINUTE, AT WHAT RATE IS THE VOLUME OF THE SNOWBALL DECREASING WHEN THE DIAMETER IS 9 CENTIMETERS? THE FIRST THING WE NEED TO REMEMBER IS THE VOLUME FORMULA FOR A SPHERE IS V=4/3 […]