Algebra 2: Expanding Cubed Binomials

Greetings math friends! This post will go over how to expand and simplify cubed binomials 2 different ways. We’re so used to seeing squared binomials such as, Screen Shot 2020-08-19 at 11.29.14 AM.png, and expanding them without a second thought.  But what happens when our reliable squared binomials are now raised to the third power, such as,Screen Shot 2020-08-19 at 11.29.48 AM?  Luckily for us, there is a Rule we can use:

Screen Shot 2020-08-18 at 10.12.33 PM

But where did this rule come from?  And how can we so blindly trust it? Which is why we are going to prove the above rule here and now using 2 different methods:Screen Shot 2020-08-19 at 11.31.13 AM

Why bother? Proving this rule will allow us to expand and simplify any cubic binomial given to us in the future! And since we are proving it 2 different ways, you can choose the method that best works for you.

Method #1: The Box MethodScreen Shot 2020-08-18 at 10.14.37 PMScreen Shot 2020-08-18 at 10.14.55 PM.pngScreen Shot 2020-08-18 at 10.15.06 PMScreen Shot 2020-08-18 at 10.15.39 PM.pngScreen Shot 2020-08-18 at 10.15.50 PM

Screen Shot 2020-08-19 at 2.24.54 PMScreen Shot 2020-08-19 at 2.53.43 PM

Screen Shot 2020-08-19 at 2.29.22 PM.pngScreen Shot 2020-08-18 at 10.17.19 PM.png

Screen Shot 2020-08-19 at 2.27.56 PMScreen Shot 2020-08-19 at 2.54.36 PM.png

Screen Shot 2020-08-18 at 10.21.05 PM.png

Method #2: The Distribution MethodScreen Shot 2020-08-18 at 10.17.54 PM.pngScreen Shot 2020-08-18 at 10.19.49 PMScreen Shot 2020-08-19 at 2.42.11 PM

Screen Shot 2020-08-18 at 10.21.05 PM.png

Now that we’ve gone over 2 different methods of cubic binomial expansion, try the following practice questions on your own using your favorite method!

Practice Questions: Expand and simplify the following.

Screen Shot 2020-08-18 at 10.21.56 PM

Solutions:

Screen Shot 2020-08-18 at 10.22.19 PM.png

Still, got questions?  No problem! Check out the video above or comment below! Happy calculating! 🙂

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**Bonus: Test your skills with this Regents question on Binomial Cubic Expansion!

 

Algebra 2: Rational Exponents

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Screen Shot 2018-12-16 at 2.23.40 PM.pngScreen Shot 2018-12-16 at 2.15.36 PMScreen Shot 2018-12-16 at 2.16.44 PMScreen Shot 2018-12-16 at 2.27.35 PM.pngScreen Shot 2018-12-16 at 2.18.33 PMScreen Shot 2018-12-16 at 2.20.42 PM.pngScreen Shot 2018-12-16 at 2.21.06 PM.pngScreen Shot 2018-12-16 at 2.22.03 PM.png

Still got questions?  Don’t hesitate to comment below for anything that still isn’t clear! 🙂

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Happy calculating! 🙂

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Algebra: 4 Ways to Factor Quadratic Equations

*If you haven’t done so, check out the video that goes over this exact problem, and don’t forget to subscribe!

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Choose the factoring method that works best for you and try the practice problems on your own below!

Practice Questions:

Screen Shot 2020-06-02 at 3.09.58 PMSolutions:

Screen Shot 2020-06-02 at 3.10.30 PM

Want a review of all the different factoring methods out there?  Check out the ones left out here (DOTS and GCF) and happy calculating! 🙂

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