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Published byMadeline Webster Modified over 3 years ago

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Factoring the Sum & Difference of Two Cubes

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This is a piece of cake, if you have perfect cubes. What are perfect cubes?

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This is a piece of cake, if you have perfect cubes. What are perfect cubes? Something times something times something. Where the something is a factor 3 times. 8 is 2 2 2, so 8 is a perfect cube. x 6 is x 2 x 2 x 2 so x 6 is a perfect cube. It is easy to see if a variable is a perfect cube, how?

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This is a piece of cake, if you have perfect cubes. What are perfect cubes? Something times something times something. Where the something is a factor 3 times. 8 is 2 2 2, so 8 is a perfect cube. x 6 is x 2 x 2 x 2 so x 6 is a perfect cube. It is easy to see if a variable is a perfect cube, how? See if the exponent is divisible by 3. Its harder for integers.

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The sum or difference of two cubes will factor into a binomial trinomial. same sign always opposite always + always opposite always + same sign

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Now we know how to get the signs, lets work on what goes inside. Cube root of 1 st term Cube root of 2 nd term Product of cube root of 1 st term and cube root of 2 nd term. Square this term to get this term.

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Try one. Make a binomial and a trinomial with the correct signs.

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Try one. Cube root of 1 st term Cube root of 2 nd term

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Try one. Square this term to get this term.

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Try one. Multiply 3x an 5 to get this term.

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Try one. Square this term to get this term.

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Try one. You did it! Dont forget the first rule of factoring is to look for the greatest common factor. I hope you took notes!

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