math project pt. 3
Storyboard Text
- Woah... That's a lot easier than I've thought!
- Yes, it's simple. Now we will factor the sum and difference between two cubes. The equation for the sum between two cubes is: a^3 + b^3 = (a + b)(a^2 - ab + b^2). The equation for the difference between two cubes is: a^3 - b^3 = (a - b)(a^2 + ab + b^2). We can factor this equation: x^3 + 125. We should find the cubic root of these numbers: (x + 5). Then we should put both of these numbers into this equation: (a^2 - ab + b^2), (x^2 - 5x + 25). However, it cannot be factored anymore. Finally, we will put both of these equations together: (x + 5)(x^2 - 5x + 25).
- Phew! I guess that's it; no more of these annoying math equations ever again...
- Nuh-uh, young man. It is not over yet! We have one more thing to finish, and that is factoring by grouping... Although it is a bit tricky, we can tackle it easily if you concentrate with me. First off, suppose that we have a cubic equation that looks like this: x^3 + 2x^2 + 3x + 6; we can divide into pairs of two and separate them using parentheses: (x^3 + 2x^2) + (3x + 6). Try to find the greatest common factor of each pair: x^2 (x+2) + 3 (x+2). Finally, put x^2 and 3 in parentheses together and put x + 2 by itself: (x^2 + 3)(x + 2).
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- Well, little fish, you've certainly helped me a whole lot. I can't thank you enough for how much you helped me!
- See, young man? Please do not ridicule me for saying this, but do not judge a book by its cover. I hope you will get a 100 in your test tomorrow! I wish you the best.
- THE END
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