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    Ex 2: The Distributive Property

    – HERE ARE SOME MORE EXAMPLES OF USING THE DISTRIBUTIVE PROPERTY TO SIMPLIFY EXPRESSIONS. IN THE FIRST EXAMPLE WE HAVE -9P x THE QUANTITY P + 2. SO, WE WANT TO DISTRIBUTE -9P, WHICH MEANS WE WANT TO MULTIPLY -9P AND P AS WELL AS -9P AND 2. SO, WE’D HAVE -9P x P + -9 x 2. WELL, -9P x P IS GOING TO BE -9P TO THE SECOND OR -9P SQUARED, AND THEN WE’LL HAVE + (-18), BUT INSTEAD OF LEAVING IT IN THIS FORM AS + AND -, IT’S MORE COMMON TO WRITE THIS AS SUBTRACTING A POSITIVE. SO, THIS IS EQUIVALENT TO -9P SQUARED – (+18).…

  • Distributive Property
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    Distributive Property

    Distributive Property, a la Shmoop. King Moneylust values gold and jewels above all else. [King Moneylust sat on a throne] One day, the king’s first steward brought him 5 gold bars and 1 precious diamond. [Steward drops 5 gold bars and a diamond for the King] His second steward entered the court, also bringing the king 5 gold bars and 1 precious diamond. Moneylust’s third steward, never one to be a trailblazer, followed suit. [Third steward drops gold bars and diamond on the floor] In he came with 5 gold bars and 1 precious diamond. Because Moneylust is a busy guy and hardly has time to sit around and count…

  • Copyright Basics: Crash Course Intellectual Property 2
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    Copyright Basics: Crash Course Intellectual Property 2

    Hi. I’m Stan Muller, this is Crash Course Intellectual Property, and today we’re going to be talking about copyright law. As you might have guessed, the law of copyright relates to the right to copy, the copy right as it relates to copies of copyrightable works. You copy? [Theme Music] Right. So, the right to copy or reproduce copyright protected works is only one of the exclusive rights granted by the law of copyright. We’re also gonna discuss what types of things can actually be copyrighted, what we call the subject matter. But first, let’s talk a little bit about the history of copyright law in the United States. Why…

  • Ex 1:  The Distributive Property
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    Ex 1: The Distributive Property

    – 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 –…

  • Ex: Simplify Exponential Expressions Using Power Property – Products to Powers
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    Ex: Simplify Exponential Expressions Using Power Property – Products to Powers

    We want to simplify the following expressions completely. The first expression is two x raised to the fourth power. Let’s first simplify this by expanding, and then we’ll simplify it again using the power property of exponents. Notice we have an exponent of four, which means we have four factors of the base, which is two x. So this is equal to two x, times two x, times two x, times two x. Once expanded, notice how we can see we have four factors of two and four factors of x, so we can write this as two to the fourth times x to the fourth, and we can evaluate…